Complete the square to solve the following quadratic equation: x2+2x−8=0 .(1 point) Responses x=10, x=−8 x equals 10 , x equals negative 8 x=−2, x=4 x equals negative 2 , x equals 4 x=−10, x=8 x equals negative 10 , x equals 8 x=2, x=−4 x equals 2 , x equals negative 4

Answer 1

To complete the square for the quadratic equation \(x^2 + 2x - 8 = 0\), follow these steps:

1. Move the constant term to the other side of the equation: \[ x^2 + 2x = 8 \]

2. To complete the square, take half of the coefficient of \(x\) (which is 2), square it, and add it to both sides. Half of 2 is 1, and squaring it gives \(1^2 = 1\): \[ x^2 + 2x + 1 = 8 + 1 \] So we have: \[ (x + 1)^2 = 9 \]

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

4. Solve for \(x\) by isolating \(x\): \[ x + 1 = 3 \quad \text{or} \quad x + 1 = -3 \] Which gives: \[ x = 3 - 1 = 2 \quad \text{and} \quad x = -3 - 1 = -4 \]

The solutions are: \[ x = 2 \quad \text{and} \quad x = -4 \]

In the provided response options, the correct one is: x equals 2, x equals negative 4.