Question 1

Which property is used to solve the equation $$x^2 = 100$ for x$?

Accepted Answer

Square root property

Question 2

Given the equation $$7x^2 + 6x + 3 = 1$, which is the correct quadratic formula setup to solve for x$?

Accepted Answer

$$x = \frac{-11 \pm \sqrt{121 - 4(7)(3)}}{2(7)}$$

Question 3

What are the solutions to the equation $$25x^2 - 36 = 0$?

Accepted Answer

$$x = 6$$ and $$x = -6$$

Question 4

A square has its sides lengthened by 6 inches, resulting in a new area of 49 square inches. What is the length of a side of the original square?

Accepted Answer

$$1$$ inch

Question 5

Solve for $$x$$: $$2x/(x^2 - 8x$$) + $$16/(x^2 - 8x$$) = $$158/(x^2 - 64$$)$$. What is the solution set?

Accepted Answer

$$\{-15, 1\}$$

Question 6

A rain gutter is made from a sheet of aluminum that is 30 inches wide. After turning up the edges, the cross-sectional area is 40 square inches. What are the possible depths of the gutter, rounded to the nearest tenth?

Accepted Answer

$$1.5$$ inches and $$13.5$$ inches

Question 7

Which of the following is a correct factorization of $$16y^2 - 5y$$ - $$80y^2 = 0$?

Accepted Answer

$$(y+1)(y-5)(16y-5) = 0$$

Question 8

Solve the radical equation $$\sqrt{9x + 9} = x + 5. $$What is the solution set?

Accepted Answer

$$\{16\}$$

Question 9

What is the solution to $$(x-7)^{3/2} = 64$?

Accepted Answer

$$x = 23$$

Question 10

Given $$25x^4$$ = $$106x^2 - 81$, what are the solutions for x$?

Accepted Answer

$$1, -1, \frac{9}{5}, -\frac{9}{5}$$

Question 11

Solve the absolute value equation $$|9x - 4| + 12 = 12. $$What is the solution set?

Accepted Answer

$$\left\{\frac{4}{9}\right\}$$

Question 12

Which method is most appropriate for solving $$x^2 + 12x + 36 = 49$?

Accepted Answer

Square root property

Question 13

If $$x^2 - 17x + 16 = 0$, which of the following are the correct solutions?

Accepted Answer

$$x = 16$$ and $$x = 1$$

Question 14

Which of the following is the correct quadratic formula?

Accepted Answer

$$x = \frac{-b \pm \sqrt{b^2$ - 4ac}}{2a}$$

Question 15

If $$x^2 + 32x + 30 = 0$, what are the solutions?

Accepted Answer

$$x = -15$$ and $$x = -1$$

Question 16

Which of the following is a valid step when solving $$x^2 = 100$ using the square root property?

Accepted Answer

$$x = \pm 10$$

Question 17

When solving $$x^2 - 17x + 16 = 0$ by factoring, which factors do you use?

Accepted Answer

$$(x-16)(x-1)$$

Question 18

If $$u = x^2$ and 25u^2$ - 106u + 81 = 0$$, what are the solutions for $$u$$?

Accepted Answer

$$u = 1$$ and $$u = \frac{9}{5}$$

Question 19

What is the first step in solving the radical equation $$\sqrt{9x + 9} = x + 5$$?

Accepted Answer

Isolate the radical term

Quadratic, Polynomial, Radical, and Absolute Value Equations: Precalculus Study Guide

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