Question

Solve the following quadratic equation using square roots: (x+12)2=9 .(1 point)
Responses

{15,9}
left brace 15 comma negative 9 right brace

{−7.5,−16.5}
left brace negative 7.5 comma negative 16.5 right brace

{−3,−21}
left brace negative 3 comma negative 21 right brace

{−9,−15}

Answer 1

To solve the equation \((x + 12)^2 = 9\) using square roots, we can follow these steps:

1. Take the square root of both sides:

\[
x + 12 = \pm 3
\]

2. Now, we separate the two cases:

**Case 1:**

\[
x + 12 = 3
\]
Subtracting 12 from both sides gives:

\[
x = 3 - 12 = -9
\]

**Case 2:**

\[
x + 12 = -3
\]
Subtracting 12 from both sides gives:

\[
x = -3 - 12 = -15
\]

Therefore, the solutions to the equation \((x + 12)^2 = 9\) are:

\[
x = -9 \quad \text{and} \quad x = -15
\]

The solution set in set notation is:

\(\{-9, -15\}\)

So the correct response is:

\(\{-9, -15\}\)