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: \[ x = -2 \quad \text{and} \quad x = -10 \]