Question

Question

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

x=−2
, x=4
x equals negative 2 , x equals 4

x=2
, x=−4
x equals 2 , x equals negative 4

x=−10
, x=8
x equals negative 10 , x equals 8

x=10
, x=−8

Answer 1

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

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

2. Take the coefficient of \( x \), which is 2, divide it by 2 to get 1, and square it to get 1: \[ (1)^2 = 1 \]

3. Add this square to both sides: \[ x^2 + 2x + 1 = 8 + 1 \] \[ x^2 + 2x + 1 = 9 \]

4. The left side now factors as: \[ (x + 1)^2 = 9 \]

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

6. Solve for \( x \): \[ x + 1 = 3 \quad \Rightarrow \quad x = 2 \] \[ x + 1 = -3 \quad \Rightarrow \quad x = -4 \]

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

The correct response from the options provided is: x=2, x=−4