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=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

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. To do this, 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 \( 1 \).
   • Add \( 1 \) to both sides: \[ x^2 + 2x + 1 = 8 + 1 \] \[ x^2 + 2x + 1 = 9 \]

4. Now, the left side can be factored: \[ (x + 1)^2 = 9 \]

5. Take the square root of both sides: \[ x + 1 = 3 \quad \text{or} \quad x + 1 = -3 \]

6. Solve for \( x \):

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

Thus, the solutions to the equation \( x^2 + 2x - 8 = 0 \) are \( x = 2 \) and \( x = -4 \).

Therefore, the correct response is:

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