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

To solve the quadratic equation \((x + 36)^2 - 38 = 251\), we can start by isolating the squared term.

1. Add 38 to both sides:

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

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

2. Take the square root of both sides. Remember to consider both the positive and negative roots:

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

\[ x + 36 = \pm 17 \]

3. Now, solve for \(x\) by separating the two cases:

Case 1:

\[ x + 36 = 17 \]

Subtract 36 from both sides:

\[ x = 17 - 36 = -19 \]

Case 2:

\[ x + 36 = -17 \]

Subtract 36 from both sides:

\[ x = -17 - 36 = -53 \]

Thus, the solutions to the equation are:

\[ x = -19 \quad \text{and} \quad x = -53 \]

Therefore, the solution set is:

\[ {-19, -53} \]

The correct response is:

\({-19, -53}\)