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, 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 \(x\) in both cases:

   • Case 1: \(x + 6 = 4\) \[ x = 4 - 6 = -2 \]
   • Case 2: \(x + 6 = -4\) \[ x = -4 - 6 = -10 \]

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

Thus, the solutions to the equation \((x + 6)^2 / 2 = 8\) are \(x = -2\) and \(x = -10\).