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

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

1. **Isolate the squared term**:

\[
(x + 36)^2 - 38 = 251
\]
\[
(x + 36)^2 = 251 + 38
\]
\[
(x + 36)^2 = 289
\]

2. **Take square roots of both sides**:

\[
x + 36 = \pm \sqrt{289}
\]
\[
x + 36 = \pm 17
\]

3. **Solve for \(x\)**:

- For the positive case:
\[
x + 36 = 17
\]
\[
x = 17 - 36
\]
\[
x = -19
\]

- For the negative case:
\[
x + 36 = -17
\]
\[
x = -17 - 36
\]
\[
x = -53
\]

So, the solutions to the equation are:

\[
\{ -19, -53 \}
\]

Thus, the correct response is:

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