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

Question

Responses

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

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

Answer 1

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

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

2. Complete the square on the left-hand side. To do this, take half of the coefficient of \( x \) (which is 2), square it, and then add it to both sides of the equation. Half of 2 is 1, and \( 1^2 = 1 \): \[ x^2 + 2x + 1 = 8 + 1 \] This simplifies to: \[ (x + 1)^2 = 9 \]

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

4. Solve for \( x \):

   • When \( x + 1 = 3 \): \[ x = 3 - 1 = 2 \]
   • When \( x + 1 = -3 \): \[ x = -3 - 1 = -4 \]

So, the solutions for the equation \( x^2 + 2x - 8 = 0 \) are: \[ x = 2 \quad \text{and} \quad x = -4 \]

Therefore, the correct response is: x=2, x=−4.