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

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

x=−10
, x=8

Answer 1

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

1. Start with the equation: \[ x^2 + 2x - 8 = 0 \]

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

3. Complete the square on the left side. Take half of the coefficient of \(x\) (which is 2), square it, and add it to both sides. Half of 2 is 1, and \(1^2 = 1\). \[ x^2 + 2x + 1 = 8 + 1 \] \[ x^2 + 2x + 1 = 9 \]

4. The left side factors as: \[ (x + 1)^2 = 9 \]

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

6. 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 \( x^2 + 2x - 8 = 0 \) are: \[ x = 2, \quad x = -4 \]

The correct answer is: x equals 2, x equals negative 4.