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 $x^2 + 2abx + b^2$?

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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