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

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

1. **Isolate the square**:
\[
(x+36)^2 - 38 = 251
\]
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 \(\sqrt{289} = 17\):
\[
x + 36 = \pm 17
\]

3. **Solve for \(x\)**:
- For the positive case:
\[
x + 36 = 17 \implies x = 17 - 36 \implies x = -19
\]
- For the negative case:
\[
x + 36 = -17 \implies x = -17 - 36 \implies x = -53
\]

Thus, the solutions are \(x = -19\) and \(x = -53\).

The correct response is:

\(\{-19, -53\}\)