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 first isolate the squared term.

Starting from the equation:
\[
(x + 36)^2 - 38 = 251
\]

Add 38 to both sides:
\[
(x + 36)^2 = 251 + 38
\]
\[
(x + 36)^2 = 289
\]

Now, we take the square root of both sides. Remember to include both the positive and negative roots:
\[
x + 36 = \pm 17
\]

This gives us two equations to solve:
1. \(x + 36 = 17\)
2. \(x + 36 = -17\)

**Solving the first equation:**
\[
x + 36 = 17
\]
Subtract 36 from both sides:
\[
x = 17 - 36
\]
\[
x = -19
\]

**Solving the second equation:**
\[
x + 36 = -17
\]
Subtract 36 from both sides:
\[
x = -17 - 36
\]
\[
x = -53
\]

Thus, the solutions are:
\[
x = -19 \quad \text{and} \quad x = -53
\]

The correct answer is:
\[
\{-19, -53\}
\]