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

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

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

3. Complete the square on the left side. To do this, take half of the coefficient of \( x \), square it, and add it to both sides. The coefficient of \( x \) is 2: \[ \left(\frac{2}{2}\right)^2 = 1 \] Add 1 to both sides: \[ x^2 + 2x + 1 = 8 + 1 \] \[ x^2 + 2x + 1 = 9 \]

4. Now, rewrite the left side as a square: \[ (x + 1)^2 = 9 \]

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

6. Solve for \( x \):

   • If \( x + 1 = 3 \), then \( x = 2 \).
   • If \( x + 1 = -3 \), then \( x = -4 \).

Thus, the solutions to the equation are: \[ x = 2 \quad \text{and} \quad x = -4 \]

So the correct answer is: x=2, x=−4 (or \( x \) equals 2, \( x \) equals negative 4).