Question

Brianne solved a quadratic equation. Her work is shown below, with Step
\[2\] missing.
What could Brianne have written as the result from Step
\[2\]?

\[\begin{aligned}
3(x+4)^2&=48
\\\\
(x+4)^2&=16&\text{Step }1
\\\\
&&\text{Step }2
\\\\
x=-8&\text{ or }x=0&\text{Step }3
\end{aligned}\]
Choose 1 answer:
Choose 1 answer:
(Choice A)
\[x^2=12\]
A
\[x^2=12\]
(Choice B)
\[x+4=\pm4\]
B
\[x+4=\pm4\]
(Choice C)
\[x^2+4=\pm4\]
C
\[x^2+4=\pm4\]
(Choice D)
\[x^2+4^2=16\]
D
\[x^2+4^2=16\]

Answer 1

To solve the equation \( (x + 4)^2 = 16 \) (as stated in Step 1), Brianne would need to take the square root of both sides to find \( x + 4 \).

The result from taking the square root of both sides of the equation \( (x + 4)^2 = 16 \) is:

\[
x + 4 = \pm 4
\]

This result leads to the subsequent steps where she solves for \( x \) by isolating it:

1. \( x + 4 = 4 \) gives \( x = 0 \).
2. \( x + 4 = -4 \) gives \( x = -8 \).

Thus, the correct choice for Step 2 is:

**(Choice B)** \( x + 4 = \pm 4 \)