Question

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

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

{−19,−53}
left brace negative 19 comma negative 53 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 will follow these steps:

1. First, isolate the squared term by adding 38 to both sides of the equation:

\[
(x + 36)^2 - 38 + 38 = 251 + 38
\]
\[
(x + 36)^2 = 289
\]

2. Next, take the square root of both sides:

\[
x + 36 = \pm \sqrt{289}
\]
\[
x + 36 = \pm 17
\]

3. Now, solve for \( x \) by considering both the positive and negative square roots:

- For the positive case:
\[
x + 36 = 17
\]
\[
x = 17 - 36
\]
\[
x = -19
\]

- For the negative case:
\[
x + 36 = -17
\]
\[
x = -17 - 36
\]
\[
x = -53
\]

So the solutions are \( x = -19 \) and \( x = -53 \).

Thus, the solution set is:

\[
\{-19, -53\}
\]

The correct response is:

\(\{-19, -53\}\)