Question

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

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 of the equation. Remember to consider both the positive and negative roots.

\[
x + 12 = \pm 3
\]

2. Now, split this into two separate equations:

**Case 1:**
\[
x + 12 = 3
\]
Subtract 12 from both sides:
\[
x = 3 - 12
\]
\[
x = -9
\]

**Case 2:**
\[
x + 12 = -3
\]
Subtract 12 from both sides:
\[
x = -3 - 12
\]
\[
x = -15
\]

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

Therefore, the final answers are \(x = -9\) and \(x = -15\).