Question

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

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

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

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

{−19,−53}

Answer 1

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

1. 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 \(\sqrt{289} = 17\), we have:
\[
x + 36 = 17 \quad \text{or} \quad x + 36 = -17
\]

3. Solve for \(x\) in both cases:
- For \(x + 36 = 17\):
\[
x = 17 - 36 = -19
\]

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

Thus, the solutions to the equation are:
\[
\{ -19, -53 \}
\]

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