Question

solve equation with square roots
(x+6)^2/2 = 8

Answer 1

To solve the equation \(\frac{(x+6)^2}{2} = 8\), 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**. Remember to consider both the positive and negative roots:
\[
x + 6 = 4 \quad \text{or} \quad x + 6 = -4
\]

3. **Solve for \(x\)** in each case:

- For \(x + 6 = 4\):
\[
x = 4 - 6 = -2
\]

- For \(x + 6 = -4\):
\[
x = -4 - 6 = -10
\]

4. **Final solutions**:
\[
x = -2 \quad \text{or} \quad x = -10
\]

Thus, the solutions to the equation are \(x = -2\) and \(x = -10\).