Question

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

Answer 1

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

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

2. **Take half of the coefficient of \( x \) (which is 2), square it, and add it to both sides. The half of 2 is 1, and squaring it gives \( 1^2 = 1 \):**
\[
x^2 + 2x + 1 = 8 + 1
\]

3. **This simplifies to:**
\[
(x + 1)^2 = 9
\]

4. **Now, take the square root of both sides:**
\[
x + 1 = \pm 3
\]

5. **Solve for \( x \):**
- For \( x + 1 = 3 \):
\[
x = 3 - 1 = 2
\]
- For \( x + 1 = -3 \):
\[
x = -3 - 1 = -4
\]

The solutions to the equation \( x^2 + 2x - 8 = 0 \) are:
\[
x = 2 \quad \text{and} \quad x = -4.
\]