College Algebra

In Exercises 75–78, list the quadrant or quadrants satisfying each condition. x^3 > 0 and y^3 <0

In Exercises 71–74, determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The ordered pair (2, 5) satisfies 3y - 2x = - 4.

Make Sense? In Exercises 67–70, determine whether each statement makes sense or does not make sense, and explain your reasoning. I used the ordered pairs (- 2, 2), (0, 0), and (2, 2) to graph a straight line.

Exercises 73–75 will help you prepare for the material covered in the next section. Rationalize the denominator: (7 + 4√2)/(2 - 5√2).

What is a conditional equation? Give an example.

In Exercises 99–106, solve each equation. 5 - 12x = 8 - 7x - [6 ÷ 3(2 + 5^3) + 5x]

The equations in Exercises 79–90 combine the types of equations we have discussed in this section. Solve each equation. Then state whether the equation is an identity, a conditional equation, or an inconsistent equation. 4x/(x + 3) - 12/(x - 3) = (4x^2 + 36)/(x^2 - 9)

In Exercises 71–78, solve each equation. Then determine whether the equation is an identity, a conditional equation, or an inconsistent equation. 4(x + 5) = 21 + 4x

In Exercises 67–70, find all values of x such that y = 0. y = 2[3x - (4x - 6)] - 5(x - 6)

Exercises 41–60 contain rational equations with variables in denominators. For each equation, a. write the value or values of the variable that make a denominator zero. These are the restrictions on the variable. b. Keeping the restrictions in mind, solve the equation. 3/(x + 2) + 2/(x - 2) = 8/(x + 2)(x - 2)

Exercises 41–60 contain rational equations with variables in denominators. For each equation, a. write the value or values of the variable that make a denominator zero. These are the restrictions on the variable. b. Keeping the restrictions in mind, solve the equation. (x - 2)/2x + 1 = (x + 1)/x

Exercises 27–40 contain linear equations with constants in denominators. Solve each equation. 5 + (x - 2)/3 = (x + 3)/8

In Exercises 1–26, solve and check each linear equation. 25 - [2 + 5y - 3(y + 2)] = - 3(2y - 5) - [5(y - 1) - 3y + 3]

In Exercises 1–26, solve and check each linear equation. 3(x - 8) = x

In Exercises 1–26, solve and check each linear equation. 3(x - 1) = 21

In Exercises 15–35, solve each equation. Then state whether the equation is an identity, a conditional equation, or an inconsistent equation. 2x/3 = 6 - x/4

Exercises 73–75 will help you prepare for the material covered in the next section. Simplify: √18 - √8

What is an identity equation? Give an example.

In Exercises 99–106, solve each equation. [(3 + 6)^2 ÷ 3] × 4 = - 54 x

The equations in Exercises 79–90 combine the types of equations we have discussed in this section. Solve each equation. Then state whether the equation is an identity, a conditional equation, or an inconsistent equation. 4/(x - 2) + 3/(x + 5) = 7/(x + 5)(x - 2)

In Exercises 71–78, solve each equation. Then determine whether the equation is an identity, a conditional equation, or an inconsistent equation. 4x + 7 = 7(x + 1) - 3x

In Exercises 61–66, find all values of x satisfying the given conditions. y1 = (2x - 1)/(x^2 + 2x - 8), y2 = 2/(x + 4), y3 = 1/(x - 2), and y1 + y2 = y3.

Exercises 41–60 contain rational equations with variables in denominators. For each equation, a. write the value or values of the variable that make a denominator zero. These are the restrictions on the variable. b. Keeping the restrictions in mind, solve the equation. 3/(2x - 2) + 1/2 = 2/(x - 1)

Exercises 41–60 contain rational equations with variables in denominators. For each equation, a. write the value or values of the variable that make a denominator zero. These are the restrictions on the variable. b. Keeping the restrictions in mind, solve the equation. 5/2x - 8/9 = 1/18 - 1/3x

Exercises 27–40 contain linear equations with constants in denominators. Solve each equation. (x + 3)/6 = 3/8 + (x - 5)/4

In Exercises 1–26, solve and check each linear equation. 16 = 3(x - 1) - (x - 7)

In Exercises 1–26, solve and check each linear equation. 7x + 4 = x + 16

In Exercises 1–26, solve and check each linear equation. 7x - 5 = 72

In Exercises 15–35, solve each equation. Then state whether the equation is an identity, a conditional equation, or an inconsistent equation. 7x + 13 = 2(2x-5) + 3x + 23

Find b such that (4x - b)/(x - 5) = 3 has a solution set given by {Ø}.

In Exercises 99–106, solve each equation. - 2{7 - [4 -2(1 - x) + 3]} = 10 - [4x - 2(x - 3)]

Evaluate x^2 - (xy - y) for x satisfying 3(x + 3)/5 = 2x + 6 and y satisfying - 2y - 10 = 5y + 18.

The equations in Exercises 79–90 combine the types of equations we have discussed in this section. Solve each equation. Then state whether the equation is an identity, a conditional equation, or an inconsistent equation. 2/x + 1/2 = 3/4

In Exercises 71–78, solve each equation. Then determine whether the equation is an identity, a conditional equation, or an inconsistent equation. 5x + 9 = 9(x + 1) - 4x

In Exercises 61–66, find all values of x satisfying the given conditions. y1 = 5/(x + 4), y2 = 3/(x + 3), y3 = (12x + 19)/(x^2 + 7x + 12). and y1 + y2 = y3.

Exercises 41–60 contain rational equations with variables in denominators. For each equation, a. write the value or values of the variable that make a denominator zero. These are the restrictions on the variable. b. Keeping the restrictions in mind, solve the equation. 2/(x - 2) = x/(x - 2) - 2

Exercises 41–60 contain rational equations with variables in denominators. For each equation, a. write the value or values of the variable that make a denominator zero. These are the restrictions on the variable. b. Keeping the restrictions in mind, solve the equation. 7/2x - 5/3x = 22/3

Exercises 27–40 contain linear equations with constants in denominators. Solve each equation. x/5 - 1/2 = x/6

In Exercises 1–26, solve and check each linear equation. 2 - (7x + 5) = 13 - 3x

In Exercises 1–26, solve and check each linear equation. 2x - 7 = 6 + x

In Exercises 1–26, solve and check each linear equation. 4x + 9 = 33

In Exercises 15–35, solve each equation. Then state whether the equation is an identity, a conditional equation, or an inconsistent equation. 2(x-4)+3(x+5)=2x-2

Find b such that (7x + 4)/b + 13 = x has a solution set given by {- 6}.

In Exercises 99–106, solve each equation. 4x + 13 - {2x - [4(x - 3) - 5]} = 2(x - 6)

Evaluate x^2 - x for the value of x satisfying 4(x - 2) + 2 = 4x - 2(2 - x).

In Exercises 71–78, solve each equation. Then determine whether the equation is an identity, a conditional equation, or an inconsistent equation. 5x + 7 = 2x + 7

In Exercises 67–70, find all values of x such that y = 0. y = 1/(5x + 5) - 3/(x + 1) + 7/5

In Exercises 61–66, find all values of x satisfying the given conditions. y1 = 5(2x - 8) - 2, y2 = 5(x - 3) + 3, and y1 = y2.

Exercises 41–60 contain rational equations with variables in denominators. For each equation, a. write the value or values of the variable that make a denominator zero. These are the restrictions on the variable. b. Keeping the restrictions in mind, solve the equation. 3/(x + 4) - 7 = - 4/(x + 4)

Exercises 41–60 contain rational equations with variables in denominators. For each equation, a. write the value or values of the variable that make a denominator zero. These are the restrictions on the variable. b. Keeping the restrictions in mind, solve the equation. 4/x = 5/2x + 3

Exercises 27–40 contain linear equations with constants in denominators. Solve each equation. 20 - x/3 = x/2

In Exercises 1–26, solve and check each linear equation. 2(x - 1) + 3 = x - 3(x + 1)

In Exercises 1–26, solve and check each linear equation. x - 5(x + 3) = 13

In Exercises 15–35, solve each equation. Then state whether the equation is an identity, a conditional equation, or an inconsistent equation. 3-5(2x + 1) - 2(x-4) = 0

In Exercises 15–35, solve each equation. Then state whether the equation is an identity, a conditional equation, or an inconsistent equation. 7(x-4) = x + 2

What is an inconsistent equation? Give an example.

In Exercises 99–106, solve each equation. 0.7x + 0.4(20) = 0.5(x + 20)

The equations in Exercises 79–90 combine the types of equations we have discussed in this section. Solve each equation. Then state whether the equation is an identity, a conditional equation, or an inconsistent equation. 4/(x^2 + 3x - 10) - 1/(x^2 + x - 6) = 3/(x^2 - x - 12)

In Exercises 71–78, solve each equation. Then determine whether the equation is an identity, a conditional equation, or an inconsistent equation. 10x + 3 = 8x + 3

In Exercises 67–70, find all values of x such that y = 0. y = (x + 6)/(3x - 12) - 5/(x - 4) - 2/3

In Exercises 61–66, find all values of x satisfying the given conditions. y1 = (x - 3)/5, y2 = (x - 5)/4, and y1 - y2 = 1.

Exercises 41–60 contain rational equations with variables in denominators. For each equation, a. write the value or values of the variable that make a denominator zero. These are the restrictions on the variable. b. Keeping the restrictions in mind, solve the equation. 1/(x - 1) + 5 = 11/(x - 1)

Exercises 27–40 contain linear equations with constants in denominators. Solve each equation. 3x/5 - (x - 3)/2 = (x + 2)/3

Exercises 27–40 contain linear equations with constants in denominators. Solve each equation. x/3 = x/2 - 2

In Exercises 1–26, solve and check each linear equation. 4(x + 9) = x

In Exercises 1–26, solve and check each linear equation. 11x - (6x - 5) = 40

In Exercises 15–35, solve each equation. Then state whether the equation is an identity, a conditional equation, or an inconsistent equation. (3x+1)/3 - 13/2 = (1-x)/4

In Exercises 15–35, solve each equation. Then state whether the equation is an identity, a conditional equation, or an inconsistent equation. 2x-5 = 7

In Exercises 35–54, solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? 1/R = 1/R1 + 1/R2 for R1

In Exercises 35–54, solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? S = P + Prt for r

In Exercises 35–54, solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? V = (1/3)Bh for B

In Exercises 35–54, solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? D = RT for R

For an international telephone call, a telephone company charges $0.43 for the first minute, $0.32 for each additional minute, and a $2.10 service charge. If the cost of a call is $5.73, how long did the person talk?

An automobile repair shop charged a customer $1182, listing $357 for parts and the remainder for labor. If the cost of labor is $75 per hour, how many hours of labor did it take to repair the car?

The length of the rectangular tennis court at Wimbledon is 6 feet longer than twice the width. If the court’s perimeter is 228 feet, what are the court’s dimensions?

A rectangular soccer field is twice as long as it is wide. If the perimeter of the soccer field is 300 yards, what are its dimensions?

You invested $20,000 in two accounts paying 1.45% and 1.59% annual interest. If the total interest earned for the year was $307.50, how much was invested at each rate?

Including a 17.4% hotel tax, your room in Chicago cost $287.63 per night. Find the nightly cost before the tax was added.

After a 20% reduction, you purchase a television for $336. What was the television’s price before the reduction?

You are choosing between two gyms. One gym offers membership for a fee of $40 plus a monthly fee of $25. The other offers membership for a fee of $15 plus a monthly fee of $30. After how many months will the total cost at each gym be the same? What will be the total cost for each gym?

In Exercises 45–47, solve each formula for the specified variable. T = (A-P)/Pr for P

In Exercises 36–43, use the five-step strategy for solving word problems. The length of a rectangular field is 6 yards less than triple the width. If the perimeter of the field is 340 yards, what are its dimensions?

In Exercises 35–54, solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? A = 2lw + 2lh + 2wh for h

In Exercises 35–54, solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? E = mc^2 for m

In Exercises 35–54, solve each formula for the specified variable. Do you recognize the formula? If so, what does it describe? A = (1/2)bh for b

A job pays an annual salary of $57,900, which includes a holiday bonus of $1500. If paychecks are issued twice a month, what is the gross amount for each paycheck?

A repair bill on a sailboat came to $2356, including $826 for parts and the remainder for labor. If the cost of labor is $90 per hour, how many hours of labor did it take to repair the sailboat?

The length of a rectangular pool is 6 meters less than twice the width. If the pool’s perimeter is 126 meters, what are its dimensions?

A rectangular swimming pool is three times as long as it is wide. If the perimeter of the pool is 320 feet, what are its dimensions?

You invested $30,000 in two accounts paying 2.19% and 2.45% annual interest. If the total interest earned for the year was $705.88, how much was invested at each rate?

Exercises 19–20 involve markup, the amount added to the dealer’s cost of an item to arrive at the selling price of that item. The selling price of a refrigerator is $1198. If the markup is 25% of the dealer’s cost, what is the dealer’s cost of the refrigerator?

Including a 10.5% hotel tax, your room in San Diego cost $216.58 per night. Find the nightly cost before the tax was added.

An electronic pass for a toll road costs $30. The toll is normally $5.00 but is reduced by 30% for people who have purchased the electronic pass. Determine the number of times the road must be used so that the total cost without the pass is the same as the total cost with the pass.

Exercises 141–143 will help you prepare for the material covered in the next section. If the width of a rectangle is represented by x and the length is represented by x + 200, write a simplified algebraic expression that models the rectangle’s perimeter.

In Exercises 45–47, solve each formula for the specified variable. vt + gt^2 = s for g

In Exercises 36–43, use the five-step strategy for solving word problems. An apartment complex has offered you a move-in special of 30% off the first month’s rent. If you pay $945 for the first month, what should you expect to pay for the second month when you must pay full price?

In Exercises 95–99, perform the indicated operations and write the result in standard form. (i^98 - i^94)/i^49

Evaluate x^2 - 2x + 2 for x = 1 + i.

In Exercises 61–64, write each complex number in standard form. (2 + 3i)^3

In Exercises 53–60, write each power of i as as i, - 1, - i, or 1. i^31

In Exercises 37–52, perform the indicated operations and write the result in standard form. (- 2 + √-4)^2

In Exercises 29–36, simplify and write the result in standard form. √-49

In Exercises 21–28, divide and express the result in standard form. 2/(3 - i)

In Exercises 9–20, find each product and write the result in standard form. (- 5 + 4i)(3 + i)

In Exercises 48–57, perform the indicated operations and write the result in standard form. 6/(5+i)

In Exercises 95–99, perform the indicated operations and write the result in standard form. (i^85 - i^83)/i^45

In Exercises 65–70, perform the indicated operation(s) and write the result in standard form. 5√-16 + 3√-81

In Exercises 61–64, write each complex number in standard form. (1 - i)^3

In Exercises 37–52, perform the indicated operations and write the result in standard form. (3√-5)(- 4√-12)

In Exercises 37–52, perform the indicated operations and write the result in standard form. 5√-16 + 3√-81

In Exercises 21–28, divide and express the result in standard form. (2 + 3i)/(2 + i)

In Exercises 9–20, find each product and write the result in standard form. (5 - 2i)^2

In Exercises 9–20, find each product and write the result in standard form. - 3i(7i - 5)

In Exercises 48–57, perform the indicated operations and write the result in standard form. (7-i)(2+3i)

In Exercises 95–99, perform the indicated operations and write the result in standard form. 8/(1 + 2/i)

In Exercises 65–70, perform the indicated operation(s) and write the result in standard form. (4 - i)^2 - (1 + 2i)^2

In Exercises 61–64, write each complex number in standard form. (1 + i)^3

In Exercises 37–52, perform the indicated operations and write the result in standard form. √-8 (√-3 - √5)

In Exercises 37–52, perform the indicated operations and write the result in standard form. √-64 - √-25

In Exercises 21–28, divide and express the result in standard form. - 6i/(3 + 2i)

In Exercises 9–20, find each product and write the result in standard form. (2 + 3i)^2

In Exercises 1–8, add or subtract as indicated and write the result in standard form. 6 - (- 5 + 4i) - (- 13 - i)

In Exercises 95–99, perform the indicated operations and write the result in standard form. (1 + i)/(1 + 2i) + (1 - i)/(1 - 2i)

In Exercises 65–70, perform the indicated operation(s) and write the result in standard form. (2 + i)^2 - (3 - i)^2

In Exercises 53–60, write each power of i as as i, - 1, - i, or 1. i^135

In Exercises 37–52, perform the indicated operations and write the result in standard form. (- 6 - √-12)/48

In Exercises 29–36, simplify and write the result in standard form. √(1^2 - 4 × 0.5 × 5)

In Exercises 21–28, divide and express the result in standard form. 8i/(4 - 3i)

In Exercises 9–20, find each product and write the result in standard form. (- 5 + i)(- 5 - i)

In Exercises 1–8, add or subtract as indicated and write the result in standard form. (3 + 2i) - (5 - 7i)

In Exercises 95–99, perform the indicated operations and write the result in standard form. 4/(2 + i)(3 - i)

In Exercises 65–70, perform the indicated operation(s) and write the result in standard form. (8 + 9i)(2 - i) - (1 - i)(1 + i)

In Exercises 53–60, write each power of i as as i, - 1, - i, or 1. i^114

In Exercises 37–52, perform the indicated operations and write the result in standard form. (- 8 + √-32)/24

In Exercises 29–36, simplify and write the result in standard form. √(3^2 - 4 × 2 × 5)

In Exercises 21–28, divide and express the result in standard form. 5i/(2 - i)

In Exercises 9–20, find each product and write the result in standard form. (3 + 5i)(3 - 5i)

In Exercises 1–8, add or subtract as indicated and write the result in standard form. (7 + 2i) + (1 - 4i)

Evaluate (x^2 + 19)/(2 - x) for x = 3i.

In Exercises 65–70, perform the indicated operation(s) and write the result in standard form. (2 - 3i)(1 - i) - (3 - i)(3 + i)

In Exercises 53–60, write each power of i as as i, - 1, - i, or 1. i^44

In Exercises 37–52, perform the indicated operations and write the result in standard form. (- 3 - √-7)^2

In Exercises 29–36, simplify and write the result in standard form. √-108

In Exercises 21–28, divide and express the result in standard form. 2i/(1 + i)

In Exercises 9–20, find each product and write the result in standard form. (7 - 5i)(- 2 - 3i)

In Exercises 48–57, perform the indicated operations and write the result in standard form. √ (-32) - √ (-18)

Write a quadratic equation in general form whose solution set is {- 3, 5}.

In Exercises 115–122, find all values of x satisfying the given conditions. y1 = 2x^2 + 5x - 4, y2 = - x^2 + 15x - 10, and y1 - y2 = 0

Solve each equation in Exercises 83–108 by the method of your choice. 1/x + 1/(x + 3) = 1/4

Solve each equation in Exercises 83–108 by the method of your choice. 9 - 6x + x^2 = 0

Solve each equation in Exercises 83–108 by the method of your choice. 5x^2 + 2 = 11x

Solve each equation in Exercises 47–64 by completing the square. 3x^2 - 5x - 10 = 0

Solve each equation in Exercises 47–64 by completing the square. x^2 - 6x - 11 = 0

In Exercises 35–46, determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial. x^2 + 3x

Solve each equation in Exercises 1 - 14 by factoring. 7 - 7x = (3x + 2)(x - 1)

Solve each equation in Exercises 73–81 by the method of your choice. 3x^2-7x+1 =0

In Exercises 127–130, solve each equation by the method of your choice. √2 x^2 + 3x - 2√2 = 0

In Exercises 115–122, find all values of x satisfying the given conditions. y1 = 2x/(x + 2), y2 = 3/(x + 4), and y1 + y2 = 1

Solve each equation in Exercises 83–108 by the method of your choice. 1/x + 1/(x + 2) = 1/3

Solve each equation in Exercises 83–108 by the method of your choice. 3x^2 - 12x + 12 = 0

Solve each equation in Exercises 83–108 by the method of your choice. 2x^2 - x = 1

Solve each equation in Exercises 47–64 by completing the square. 3x^2 - 2x - 2 = 0

Solve each equation in Exercises 47–64 by completing the square. x^2 + 4x = 12

In Exercises 35–46, determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial. x^2 - 10x

Solve each equation in Exercises 1 - 14 by factoring. 2x(x - 3) = 5x^2 - 7x

In Exercises 71–72, without solving the given quadratic equation, determine the number and type of solutions. 9x^2 = 2-3x

In Exercises 127–130, solve each equation by the method of your choice. 1/(x^2 - 3x + 2) = 1/(x + 2) + 5/(x^2 - 4)

In Exercises 115–122, find all values of x satisfying the given conditions. y1 = x - 1, y2 = x + 4 and y1y2 = 14

Solve each equation in Exercises 83–108 by the method of your choice. 2x^2 - 7x = 0

Solve each equation in Exercises 83–108 by the method of your choice. (3x - 4)^2 = 16

In Exercises 75–82, compute the discriminant. Then determine the number and type of solutions for the given equation. x^2 - 3x - 7 = 0

Solve each equation in Exercises 47–64 by completing the square. 4x^2 - 4x - 1 = 0

Solve each equation in Exercises 47–64 by completing the square. x^2 - 2x = 2

Solve each equation in Exercises 15–34 by the square root property. 2x^2 - 5 = - 55

Solve each equation in Exercises 1 - 14 by factoring. 3x^2 + 12x = 0

Solve each equation in Exercises 68–70 using the quadratic formula. 2x^2 = 3-4x

When the sum of 1 and twice a negative number is subtracted from twice the square of the number, 0 results. Find the number.

In Exercises 115–122, find all values of x satisfying the given conditions. y = 5x^2 + 3x and y = 2

Solve each equation in Exercises 83–108 by the method of your choice. x^2 = 4x - 7

Solve each equation in Exercises 83–108 by the method of your choice. (2x - 5)(x + 1) = 2

In Exercises 75–82, compute the discriminant. Then determine the number and type of solutions for the given equation. x^2 - 2x + 1 = 0

Solve each equation in Exercises 47–64 by completing the square. 2x^2 - 7x + 3 = 0

Solve each equation in Exercises 47–64 by completing the square. x^2 + 6x = 7

Solve each equation in Exercises 15–34 by the square root property. 3x^2 - 1 = 47

Solve each equation in Exercises 1 - 14 by factoring. 3x^2 - 2x = 8

Solve each equation in Exercises 66–67 by completing the square. 3x^2 -12x+11= 0

When the sum of 6 and twice a positive number is subtracted from the square of the number, 0 results. Find the number.

In Exercises 115–122, find all values of x satisfying the given conditions. y = 2x^2 - 3x and y = 2

Solve each equation in Exercises 83–108 by the method of your choice. x^2 - 4x + 29 = 0

Solve each equation in Exercises 83–108 by the method of your choice. (2x + 3)(x + 4) = 1

In Exercises 75–82, compute the discriminant. Then determine the number and type of solutions for the given equation. 2x^2 - 11x + 3 = 0

Solve each equation in Exercises 47–64 by completing the square. x^2 + 3x - 1 = 0

In Exercises 35–46, determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial. x^2 - (1/3)x

Solve each equation in Exercises 15–34 by the square root property. 5x^2 = 45

Exercises 100–102 will help you prepare for the material covered in the next section. Factor: x^2 - 6x + 9

In Exercises 64–65, determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial. x^2+ 20x

In Exercises 123–124, list all numbers that must be excluded from the domain of each rational expression. 3/(2x^2 + 4x - 9)

Solve each equation in Exercises 83–108 by the method of your choice. 3/(x - 3) + 5/(x - 4) = (x^2 - 20)/(x^2 - 7x + 12)

Solve each equation in Exercises 83–108 by the method of your choice. x^2 - 6x + 13 = 0

Solve each equation in Exercises 83–108 by the method of your choice. x^2 - 2x = 1

In Exercises 75–82, compute the discriminant. Then determine the number and type of solutions for the given equation. x^2 - 4x - 5 = 0

Solve each equation in Exercises 47–64 by completing the square. x^2 - 5x + 6 = 0

In Exercises 35–46, determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial. x^2 - (2/3)x

Solve each equation in Exercises 15–34 by the square root property. 3x^2 = 27

Exercises 73–75 will help you prepare for the material covered in the next section. Multiply: (7 - 3x)(- 2 - 5x)

Solve each equation in Exercises 60–63 by the square root property. x^2/2 + 5 = -3

In Exercises 115–122, find all values of x satisfying the given conditions. y1 = - x^2 + 4x - 2, y2 = - 3x^2 + x - 1, and y1 - y2 = 0

Solve each equation in Exercises 83–108 by the method of your choice. 2x/(x - 3) + 6/(x + 3) = - 28/(x^2 - 9)

Solve each equation in Exercises 83–108 by the method of your choice. 4x^2 - 16 = 0

Solve each equation in Exercises 83–108 by the method of your choice. 3x^2 = 60

Solve each equation in Exercises 65–74 using the quadratic formula. x^2 - 6x + 10 = 0

Solve each equation in Exercises 47–64 by completing the square. x^2 + 4x + 1 = 0

In Exercises 35–46, determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial. x^2 - 7x

Solve each equation in Exercises 1 - 14 by factoring. 10x - 1 = (2x + 1)^2

Solve each equation in Exercises 73–81 by the method of your choice. (x-3)^2 - 25 = 0

Solve each equation in Exercises 58–59 by factoring. 2x^2 +15x = 8

Solve for x: x^(5/6) + x^(2/3) - 2x^(1/2) = 0

If 5 times a number is decreased by 4, the principal square root of this difference is 2 less than the number. Find the number(s).

In Exercises 91–100, find all values of x satisfying the given conditions. y = x^3 + 4x^2 - x + 6 and y = 10

The rule for rewriting an absolute value equation without absolute value bars can be extended to equations with two sets of absolute value bars: If u and v represent algebraic expressions, then |u| = |v| is equivalent to u = v or u = - v. Use this to solve the equations in Exercises 77–84. |3x - 1| = |x + 5|

In Exercises 61–76, solve each absolute value equation or indicate that the equation has no solution. |2x - 1| = 5

Solve each equation in Exercises 41–60 by making an appropriate substitution. 9x^4 = 25x^2 - 16

Solve each radical equation in Exercises 11–30. Check all proposed solutions. √(x + 8) - √(x - 4) = 2

Solve each polynomial equation in Exercises 1–10 by factoring and then using the zero-product principle. 4x^3 - 12x^2 = 9x - 27

Solve the equations containing absolute value in Exercises 94–95. |2x+1| = 7

Solve for x: ∛(x√x) = 9

In Exercises 101–106, solve each equation. x(x + 1)^3 - 42(x + 1)^2 = 0

In Exercises 91–100, find all values of x satisfying the given conditions. y = x - √(x - 2) and y = 4

In Exercises 61–76, solve each absolute value equation or indicate that the equation has no solution. |2x - 1| + 3 = 3

In Exercises 61–76, solve each absolute value equation or indicate that the equation has no solution. |x - 2| = 7

Solve each equation with rational exponents in Exercises 31–40. Check all proposed solutions. (x^2 - x - 4)^(3/4) - 2 = 6

Solve each radical equation in Exercises 11–30. Check all proposed solutions. √(2x + 19) - 8 = x

Solve each polynomial equation in Exercises 1–10 by factoring and then using the zero-product principle. 5x^4 - 20x^2 = 0

Solve each equation in Exercises 92–93 by making an appropriate substitution. x^4 - 5x^2 + 4 = 0

Solve without squaring both sides: 5 - (2/x) = √(5 - 2/x).

In Exercises 101–106, solve each equation. |x^2 + 2x - 36| = 12

In Exercises 91–100, find all values of x satisfying the given conditions. y = |2 - 3x| and y = 13

In Exercises 61–76, solve each absolute value equation or indicate that the equation has no solution. |x + 1| + 5 = 3

Solve each equation in Exercises 41–60 by making an appropriate substitution. (x - 5)^2 - 4(x - 5) - 21 = 0

Solve each equation with rational exponents in Exercises 31–40. Check all proposed solutions. (x - 4)^(2/3) = 16

Solve each radical equation in Exercises 11–30. Check all proposed solutions. √(6x + 1) = x - 1

Exercises 177–179 will help you prepare for the material covered in the next section. If - 8 is substituted for x in the equation 5x^(2/3) + 11x^(1/3) + 2 = 0, is the resulting statement true or false?

Solve each radical equation in Exercises 88–89. √ (2x-3) + x = 3

Solve: √(6x - 2) = √(2x + 3) - √(4x - 1).