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

Answer 1

To solve the quadratic equation \((x + 6)^2/2 = 8\) using square roots, you 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 isolating it in two cases:

   • Case 1: \[ x + 6 = 4 \implies x = 4 - 6 = -2 \]

   • Case 2: \[ x + 6 = -4 \implies x = -4 - 6 = -10 \]

4. Combine the solutions: The two solutions for the equation are: \[ x = -2 \quad \text{and} \quad x = -10 \]

Thus, the solutions to the equation \((x + 6)^2/2 = 8\) are: \[ \boxed{-2} \quad \text{and} \quad \boxed{-10} \]