Complete the square to solve the following quadratic equation: x^2+2x−8=0.(1 point)

To solve the quadratic equation \(x^2 + 2x - 8 = 0\) by completing the square, we follow these steps:

1. Rearrange the equation:
   \[ x^2 + 2x = 8 \]

2. Complete the square on the left side. Take half of the coefficient of \(x\) (which is \(2\)), square it, and add it to both sides:
   \[ \left(\frac{2}{2}\right)^2 = 1 \]
   So we add \(1\) to both sides:
   \[ x^2 + 2x + 1 = 8 + 1 \]
   This simplifies to:
   \[ (x + 1)^2 = 9 \]

3. Take the square root of both sides:
   \[ x + 1 = \pm 3 \]

4. Solve for \(x\) by isolating \(x\):

   • For the positive case:
     \[ x + 1 = 3 \quad \Rightarrow \quad x = 3 - 1 = 2 \]
   • For the negative case:
     \[ x + 1 = -3 \quad \Rightarrow \quad x = -3 - 1 = -4 \]

Thus, the solutions are \(x = 2\) and \(x = -4\).

The correct response is: x = 2, x = -4.