Complete the square to solve the following quadratic equation: x2+2x−8=0.(1 point)
To complete the square for the quadratic equation x^2 + 2x - 8 = 0, follow these steps:
1. Move the constant term to the other side of the equation:
x^2 + 2x = 8
2. Take half of the coefficient of x and square it. In this case, (2/2)^2 = 1.
Add this value to both sides of the equation:
x^2 + 2x + 1 = 8 + 1
Simplifying:
x^2 + 2x + 1 = 9
3. Rewrite the left side of the equation as a perfect square:
(x + 1)^2 = 9
4. Take the square root of both sides (remember to include both positive and negative roots):
x + 1 = ±√9
5. Simplify the right side:
x + 1 = ±3
6. Solve for x by subtracting 1 from both sides:
x = -1 ± 3
This yields two solutions:
x = -1 + 3 = 2
x = -1 - 3 = -4
So, the solutions to the quadratic equation x^2 + 2x - 8 = 0 are x = 2 and x = -4.