1. Equations & Inequalities

The Square Root Property

1. Equations & Inequalities

# The Square Root Property - Video Tutorials & Practice Problems

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concept

## Solving Quadratic Equations by the Square Root Property

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2

Problem

ProblemSolve the given quadratic equation using the square root property. $\left(x-\frac12\right)^2-5=0$

A

$x=\frac12+\sqrt5,x=\frac12-\sqrt5$

B

$x=\frac52,x=-\frac52$

C

$x=\frac{\sqrt5}{2},x=-\frac{\sqrt5}{2}$

D

$x=\frac12,x=-\frac12$

3

Problem

ProblemSolve the given quadratic equation using the square root property. $2x^2-16=0$

A

$x=0,x=-2$

B

$x=4\sqrt2,x=-4\sqrt2$

C

$x=4,x=-4$

D

$x=2\sqrt2,x=-2\sqrt2$

4

concept

## Imaginary Roots with the Square Root Property

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PRACTICE PROBLEMS AND ACTIVITIES (37)

- Solve each equation in Exercises 1 - 14 by factoring. x^2 - 3x - 10 = 0
- Match the equation in Column I with its solution(s) in Column II. x^2 + 5 = 0
- Use Choices A–D to answer each question. A. 3x^2 - 17x - 6 = 0 B. (2x + 5)^2 = 7 C. x^2 + x = 12 D. (3x - 1)(x...
- Answer each question. Answer each question. Answer each question. Unknown NumbersUse the following facts.If x ...
- Solve each equation using the zero-factor property. See Example 1. x^2 + 2x - 8 = 0
- Solve each equation in Exercises 1 - 14 by factoring. 10x - 1 = (2x + 1)^2
- Answer each question. Answer each question. Answer each question. Unknown NumbersUse the following facts.If x ...
- Solve each equation using the zero-factor property. See Example 1. x^2 - 64 = 0
- Solve each equation in Exercises 15–34 by the square root property. (x + 3)^2 = - 16
- Volume of a Box. A rectangular piece of metal is 10 in. longer than it is wide. Squares with sides 2 in. long ...
- Solve each equation using the square root property. See Example 2. 27 - x^2 = 0
- Dimensions of a SquareWhat is the length of the side of a square if its area and perimeter are numerically equ...
- Solve each equation using the square root property. See Example 2. (4x + 1)^2 = 20
- Solve each equation using the square root property. See Example 2. (-2x + 5)^2 = -8
- In Exercises 35–46, determine the constant that should be added to the binomial so that it becomes a perfect s...
- Solve each equation. 2x²+x-15 = 0
- Solve each equation. x²- √5x -1 = 0
- Solve each equation using completing the square. See Examples 3 and 4. -2x^2 + 4x + 3 = 0
- Solve each equation in Exercises 47–64 by completing the square. x^2 + 4x = 12
- Evaluate the discriminant for each equation. Then use it to determine the number and type of solutions. -8x² +...
- Solve each equation using the quadratic formula. See Examples 5 and 6. x^2 - 3x - 2 = 0
- Solve each equation using the quadratic formula. See Examples 5 and 6. 1/2x^2 + 1/4x - 3 = 0
- Solve each equation in Exercises 47–64 by completing the square. 3x^2 - 2x - 2 = 0
- Solve each equation using the quadratic formula. See Examples 5 and 6. (3x + 2)(x - 1) = 3x
- Solve each equation in Exercises 66–67 by completing the square. 3x^2 -12x+11= 0
- Solve each equation for the specified variable. (Assume no denominators are 0.) See Example 8. F = kMv^2/r , f...
- In Exercises 75–82, compute the discriminant. Then determine the number and type of solutions for the given eq...
- For each equation, (a) solve for x in terms of y.. See Example 8. 4x^2 - 2xy + 3y^2 = 2
- Evaluate the discriminant for each equation. Then use it to determine the number of distinct solutions, and te...
- Evaluate the discriminant for each equation. Then use it to determine the number of distinct solutions, and te...
- Solve each equation in Exercises 83–108 by the method of your choice. x^2 - 2x = 1
- Answer each question. Find the values of a, b, and c for which the quadratic equation. ax^2 + bx + c = 0 has ...
- 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. 3/(x - 3) + 5/(x - 4) = (x^2 - 20)/(x^2...
- In Exercises 115–122, find all values of x satisfying the given conditions. y1 = 2x/(x + 2), y2 = 3/(x + 4), ...
- In Exercises 123–124, list all numbers that must be excluded from the domain of each rational expression. 3/(...
- In Exercises 127–130, solve each equation by the method of your choice. √2 x^2 + 3x - 2√2 = 0