Question

Complete the square to solve the following quadratic equation: x^2 + 2x - 8 = 0

Answer 1

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

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

2. **Complete the square:**
- Take the coefficient of \( x \) (which is 2), divide it by 2 to get 1, and then square it to get \( 1^2 = 1 \).
- Add this square to both sides of the equation:
\[
x^2 + 2x + 1 = 8 + 1
\]
\[
x^2 + 2x + 1 = 9
\]

3. **Rewrite the left side as a squared term:**
\[
(x + 1)^2 = 9
\]

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

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

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