Question

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

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

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

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

{−7.5,−16.5}

Answer 1

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

1. Take the square root of both sides:
\[
x + 12 = \pm 3
\]

2. This gives us two separate equations to solve:
\[
x + 12 = 3 \quad \text{and} \quad x + 12 = -3
\]

3. Solve each equation for \(x\):

- For \(x + 12 = 3\):
\[
x = 3 - 12
\]
\[
x = -9
\]

- For \(x + 12 = -3\):
\[
x = -3 - 12
\]
\[
x = -15
\]

Thus, the solutions to the equation \((x + 12)^2 = 9\) are:
\[
x = -9 \quad \text{and} \quad x = -15
\]

Therefore, the solution set is \(\{-9, -15\}\).

The correct response is:
\(\{-9, -15\}\)