Question

A) Solve the following quadratic equation using square roots: (x + 12)
2 = 9. (1 point)
{−7.5, − 16.5}
{−3, − 21}
{15, 9}
{−9, − 15

Answer 1

To solve the quadratic 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. Solve for \(x\) in both cases:

a) For the positive root:
\[
x + 12 = 3 \implies x = 3 - 12 \implies x = -9
\]

b) For the negative root:
\[
x + 12 = -3 \implies x = -3 - 12 \implies x = -15
\]

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

The correct answer is \(\{-9, -15\}\).