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

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

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

{−7.5,−16.5}

Answer 1

To solve the quadratic equation \((x + 12)^2 = 9\) using square roots, we first take the square root of both sides:

\[
x + 12 = \pm 3
\]

This gives us two cases to consider:

1. \(x + 12 = 3\)
2. \(x + 12 = -3\)

**For the first case:**
\[
x + 12 = 3
\]
Subtracting 12 from both sides:
\[
x = 3 - 12
\]
\[
x = -9
\]

**For the second case:**
\[
x + 12 = -3
\]
Subtracting 12 from both sides:
\[
x = -3 - 12
\]
\[
x = -15
\]

Therefore, the solutions to the equation are:
\[
x = -9 \quad \text{and} \quad x = -15
\]

So, the answer is:
\(\{-9, -15\}\).

Thus, the correct response is:
**{−9,−15}**.