Solve the following quadratic equation using square roots: (x+36)^2 − 38=251 .(1 point)

To solve the quadratic equation \((x + 36)^2 - 38 = 251\), we can follow these steps:

1. **Isolate the squared term**:
\[
(x + 36)^2 - 38 = 251
\]
Add 38 to both sides:
\[
(x + 36)^2 = 251 + 38
\]
\[
(x + 36)^2 = 289
\]

2. **Take the square root of both sides**:
\[
x + 36 = \pm \sqrt{289}
\]
Since \(\sqrt{289} = 17\):
\[
x + 36 = 17 \quad \text{or} \quad x + 36 = -17
\]

3. **Solve for \(x\)**:
- For \(x + 36 = 17\):
\[
x = 17 - 36
\]
\[
x = -19
\]

- For \(x + 36 = -17\):
\[
x = -17 - 36
\]
\[
x = -53
\]

4. **Final solution**:
\[
x = -19, -53
\]

The solution set is \(\{-19, -53\}\).

So, the correct response is:
\(\{-19, -53\}\)