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

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

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

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

Answer 1

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

1. Start by adding 38 to both sides:

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

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

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

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

Since \(\sqrt{289} = 17\):

\[
x + 36 = 17 \quad \text{or} \quad x + 36 = -17
\]

3. Now, solve for \(x\):

- For \(x + 36 = 17\):

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

- For \(x + 36 = -17\):

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

Thus, the solutions to the equation are:

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

So, the final answer is:

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

This corresponds to the last option:

{−19,−53}