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

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

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

{−1.17,−6.83}

Answer 1

To solve the quadratic equation \((x+6)^2/2 = 8\) using square roots, follow these steps:

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 \(x\)** in each case:

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

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

4. **Combine the solutions**:

The solutions are \(x = -2\) and \(x = -10\).

Thus, the solution set is \(\{-2, -10\}\).

The correct response is:
\[
\{-2, -10\}
\]