Question

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=2, x=−4 x equals 2 , x equals negative 4 x=−10, x=8

Answer 1

To complete the square, we want to rewrite the quadratic equation in the form: (x + a)^2 = b.

To do this, take half of the coefficient of x and square it, which is 2/2 = 1. Add 1 to both sides of the equation:

x^2 + 2x − 8 + 1 = 1
x^2 + 2x − 7 = 1

Now, factor the left side of the equation:

(x + 1)^2 = 9

Taking the square root of both sides:

x + 1 = ±3

Subtracting 1 from both sides:

x = -1 ± 3

This gives us two possible solutions:

x = -1 + 3 = 2
x = -1 - 3 = -4

Therefore, the correct solution is x = 2, x = -4.