Question

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

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

​ {−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

{−1.17,−6.83}

Answer 1

To solve the quadratic equation \(\frac{(x+6)^2}{2} = 8\), we can 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 \(x\)** by splitting it 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:
\[
x = -4 - 6 = -10
\]

4. **Final Solutions**:
The solutions to the equation are:
\[
x = -2 \quad \text{and} \quad x = -10
\]

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

The correct response is:
**{−2,−10}**.