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

Question

.(1 point)
Responses

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

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

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

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

Answer 1

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

1. Move the constant term to the right side of the equation:

   \[ x^2 + 2x = 8 \]

2. Take half of the coefficient of \(x\) (which is 2), square it, and add it to both sides. 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 \(x\):

   • For the positive case:

     \[ x + 1 = 3 \quad \Rightarrow \quad x = 3 - 1 = 2 \]

   • For the negative case:

     \[ x + 1 = -3 \quad \Rightarrow \quad x = -3 - 1 = -4 \]

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

The correct response is:

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