Question

Solve the following quadratic equation using square roots: (x+6)^2/2=8
.(1 point)
Responses

​ {−0.34,−11.66}
​ left brace negative 0.34 comma negative 11.66 right brace

{−2,−10}
left brace negative 2 comma negative 10 right brace

{10,−22}
left brace 10 comma negative 22 right brace

{−1.17,−6.83}
left brace negative 1.17 comma negative 6.83 right brace

Answer 1

To solve the quadratic equation \(\frac{(x+6)^2}{2} = 8\), we will first isolate the squared term and then solve for \(x\).

1. Multiply both sides by \(2\) to eliminate the fraction:

\[
(x+6)^2 = 16
\]

2. Take the square root of both sides:

\[
x + 6 = \pm 4
\]

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

- For the positive case:
\[
x + 6 = 4 \implies x = 4 - 6 = -2
\]

- For the negative case:
\[
x + 6 = -4 \implies x = -4 - 6 = -10
\]

Thus, the solutions for the equation are:

\[
\{ -2, -10 \}
\]

Therefore, the correct response is:

**{−2,−10}**