Question

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

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

1. **Take the square root of both sides**:
\[
x + 3 = \pm \sqrt{36}
\]

2. **Calculate the square root**:
\[
x + 3 = \pm 6
\]

3. **Solve for \(x\) for both cases**:
- Case 1:
\[
x + 3 = 6
\]
Subtract 3 from both sides:
\[
x = 6 - 3 = 3
\]

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

4. **The solutions are**:
\[
x = 3 \quad \text{and} \quad x = -9
\]

Thus, the final solutions to the equation \((x + 3)^2 = 36\) are \(x = 3\) and \(x = -9\).