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

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

{53,19}

Answer 1

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

1. First, isolate the squared term:
\[
(x + 36)^2 - 38 = 251
\]
Add 38 to both sides:
\[
(x + 36)^2 = 251 + 38
\]
\[
(x + 36)^2 = 289
\]

2. Now, take the square root of both sides:
\[
x + 36 = \pm \sqrt{289}
\]
The square root of 289 is 17, so:
\[
x + 36 = 17 \quad \text{or} \quad x + 36 = -17
\]

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

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

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

The solution set is:
\[
\{-19, -53\}
\]

So the correct response is:
\(\{-19, -53\}\)