Question 1

Which of the following is the correct first step to solve $$x^2 + 6x - 7 = 0$ by completing the square?

Accepted Answer

Add 7 to both sides to get $$x^2 + 6x = 7$.

Question 2

What is the value that should be added to both sides to complete the square for $$x^2 + 4x = 15$?

Accepted Answer

$$\left(\frac{4}{2}\$$right)^2$$ = 4$$

Question 3

After completing the square, which equation correctly represents $$x^2 + 6x - 7 = 0$?

Accepted Answer

$$(x + 3)^2$ = 16$$

Question 4

Which property allows you to solve $$(x + 3)^2$ = 2$$ for $$x$$?

Accepted Answer

Square Root Property

Question 5

Given $$x^2 + bx + c = 0$, what is the formula for the constant to add when completing the square?

Accepted Answer

$$\left(\frac{b}{2}\$$right)^2$$

Question 6

Solve $$x^2 + 3x - 5 = 0$ by completing the square. What is the value of x$?

Accepted Answer

$$x = -\frac{3}{2} \pm \sqrt{\frac{29}{4}}$$

Question 7

Which of the following is NOT a valid method for solving $$ax^2 + bx + c = 0$?

Accepted Answer

Multiplying both sides by $$x$$

Question 8

A chemical reaction's rate is modeled by $$x^2 - 6x + 9 = 0$. What is the solution for x$?

Accepted Answer

$$x = 3$$

Question 9

If $$x^2 + bx + c = 0$ is rewritten as (x$$ + $$d)^2 = k$, what is the value of d$?

Accepted Answer

$$d = \frac{b}{2}$$

Question 10

A medical dosage formula is modeled by $$3x^2 - 6x - 9 = 0$. What is the first step to solve by completing the square?

Accepted Answer

Divide both sides by 3 to get $$x^2 - 2x - 3 = 0$

Question 11

After completing the square for $$x^2 + 4x = 15$, what is the next step?

Accepted Answer

Take the square root of both sides

Question 12

Which equation represents the perfect square trinomial for $$x^2 + 2$$abx + $$b^2$$?

Accepted Answer

$$(x + b)^2$

Question 13

A quadratic equation $$x^2 + bx + c = 0$ is solved by completing the square. Which step comes immediately after adding $$\left(\frac{b}{2}\$$right)^2 to $$both sides?

Accepted Answer

Factor the left side as a perfect square trinomial

Question 14

If $$(x + 3)^2$ = 2$$, what are the solutions for $$x$$?

Accepted Answer

$$x = -3 \pm \sqrt{2}$$

Question 15

Which of the following is the correct sequence for completing the square?

Accepted Answer

Simplify, add $$\left(\frac{b}{2}\$$right)^2$$, factor, solve using square root property

Question 16

A quadratic equation models the height of a projectile: $$x^2 + 8x + 12 = 0$. What is the value to add to both sides to complete the square?

Accepted Answer

$$16$$

Question 17

Which method is most appropriate for solving $$x^2 + bx = c$ when b$ and c$ are real numbers and factoring is not possible?

Accepted Answer

Completing the square

Question 18

If $$x^2 + 6x = 7$, what is the completed square form?

Accepted Answer

$$(x + 3)^2$ = 16$$

Question 19

A quadratic equation $$x^2 + bx + c = 0$ is solved by completing the square. What is the general solution for x$?

Accepted Answer

$$x = -\frac{b}{2} \pm \sqrt{\left(\frac{b}{2}\$$right)^2$$ - c}$$

Solving Quadratic Equations: Completing the Square

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