Question

Solve the following quadratic equation using square roots (x+6)^2/2=8

Answer 1

To solve the quadratic equation \((x + 6)^2 / 2 = 8\), 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**. Keep in mind that this will give us both the positive and negative roots:
\[
x + 6 = \pm 4
\]

3. **Solve for \(x\)** by splitting into two equations:

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

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

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