Complete the square to solve the following quadratic equation: x2+2x−8=0.(1 point)

Question

Complete the square to solve the following quadratic equation: x2+2x−8=0.(1 point)
Responses

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

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

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

x=−2, x=4

GPT-4o mini · Answer

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. To 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: $$ 1^2 = 1 $$ 4. Add 1 to both sides: $$ x^2 + 2x + 1 = 8 + 1 $$ $$ x^2 + 2x + 1 = 9 $$ 5. Now, the left side can be factored as a perfect square: $$ (x + 1)^2 = 9 $$ 6. Take the square root of both sides: $$ x + 1 = 3 \quad \text{or} \quad x + 1 = -3 $$ 7. Solve for $x$: $$ x + 1 = 3 \implies x = 2 $$ $$ x + 1 = -3 \implies x = -4 $$ So the solutions to the equation $x^2 + 2x - 8 = 0$ are: $$ x = 2 \quad \text{and} \quad x = -4 $$ The correct response is: **x equals 2, x equals negative 4**.