Question

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

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

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

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

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

Answer 1

To solve the equation \(\frac{(x+6)^2}{2}=8\), we start by eliminating the fraction:

1. Multiply both sides by 2:
\[
(x + 6)^2 = 16
\]

2. Next, take the square root of both sides:
\[
x + 6 = \pm 4
\]

3. Now we can solve for \(x\) by separating into two cases:

**Case 1:**
\[
x + 6 = 4
\]
Subtract 6 from both sides:
\[
x = 4 - 6 = -2
\]

**Case 2:**
\[
x + 6 = -4
\]
Subtract 6 from both sides:
\[
x = -4 - 6 = -10
\]

Thus, the solutions to the equation are:
\[
\{ -2, -10 \}
\]

So, the correct response is:
\[
\{−2,−10\}
\]