Question

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

{−7.5, −16.5}
{−7.5, −16.5}

{−9,−15}
start set negative 9 comma negative 15 end set

{15, 9}
{15, 9}

{−3, −21}
{−3, −21}

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. Solve for \(x\) for both cases:

- First case:
\[
x + 12 = 3 \implies x = 3 - 12 = -9
\]

- Second case:
\[
x + 12 = -3 \implies x = -3 - 12 = -15
\]

So the solutions are \(x = -9\) and \(x = -15\).

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