Question

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

{−19,−53}
left brace negative 19 comma negative 53 right brace

{253,−325}
left brace 253 comma negative 325 right brace

{53,19}
left brace 53 comma 19 right brace

{17.84,−13.84}
left brace 17.84 comma negative 13.84 right brace

Answer 1

To solve the equation \((x + 36)^2 - 38 = 251\), we'll first isolate the squared term.

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

2. Next, take the square root of both sides:
\[
x + 36 = \pm \sqrt{289}
\]
Since \(\sqrt{289} = 17\):
\[
x + 36 = \pm 17
\]

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

4. Solve each equation:

For \(x + 36 = 17\):
\[
x = 17 - 36
\]
\[
x = -19
\]

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

5. Therefore, the solutions to the equation are:
\[
x = -19 \quad \text{and} \quad x = -53
\]

Thus, the correct response is:
\[
\{-19, -53\}
\]