Complete the square to solve the following quadratic equation: x2+2x−8=0

Question

.(1 point)
Responses

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

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

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

x=−10
, x=8

Answer 1

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

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

2. 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 \( 1^2 = 1 \).

   Add 1 to both sides:
   \[ x^2 + 2x + 1 = 8 + 1 \] Simplifying gives:
   \[ (x + 1)^2 = 9 \]

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

4. Solve for \( x \):

   a) \( x + 1 = 3 \):
   \[ x = 2 \]

   b) \( x + 1 = -3 \):
   \[ x = -4 \]

Thus, the solutions are \( x = 2 \) and \( x = -4 \).

The correct response is: x = 2, x = -4.