To solve the quadratic equation \((x + 12)^2 = 9\) using square roots, follow these steps:
- Take the square root of both sides of the equation. Remember to consider both the positive and negative roots.
\[ x + 12 = \pm 3 \]
- 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: \[ x = -3 - 12 \] \[ x = -15 \]
- 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 \(x = -15\).