Question

Solve the following quadratic equation using square roots: (x+3)2=36.(1 point)

Answer 1

To solve the equation \((x + 3)^2 = 36\) using square roots, follow these steps:

1. Take the square root of both sides:
\[
x + 3 = \pm 6
\]

2. Solve for \(x\) by considering both the positive and negative cases:

- **Case 1**:
\[
x + 3 = 6
\]
Subtracting 3 from both sides gives:
\[
x = 6 - 3 = 3
\]

- **Case 2**:
\[
x + 3 = -6
\]
Subtracting 3 from both sides gives:
\[
x = -6 - 3 = -9
\]

3. Therefore, the solutions to the equation \((x + 3)^2 = 36\) are:
\[
x = 3 \quad \text{and} \quad x = -9
\]

So, the final answers are \(x = 3\) and \(x = -9\).