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 x equals negative 10 , x equals 8
To complete the square, we need to rearrange the equation by moving the constant term to the right side:
x^2 + 2x = 8
Now, take half of the coefficient of x (which is 2) and square it. Add this value to both sides of the equation:
x^2 + 2x + (2/2)^2 = 8 + (2/2)^2
x^2 + 2x + 1 = 8 + 1
x^2 + 2x + 1 = 9
The left side of the equation can be written as a perfect square:
(x + 1)^2 = 9
Taking the square root of both sides:
√((x + 1)^2) = ±√9
x + 1 = ±3
Solving for x:
x = -1 + 3 = 2 or x = -1 - 3 = -4
Therefore, x equals 2 and x equals -4 are the solutions to the equation x^2 + 2x - 8 = 0.