Question

complete 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, follow these steps:

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

2. **Take the coefficient of \( x \), divide it by 2, and square it:**
The coefficient of \( x \) is \( 2 \).
\[
\left(\frac{2}{2}\right)^2 = 1
\]

3. **Add and subtract this square on the left side:**
\[
x^2 + 2x + 1 - 1 = 8
\]
\[
(x + 1)^2 - 1 = 8
\]

4. **Combine like terms:**
\[
(x + 1)^2 = 8 + 1
\]
\[
(x + 1)^2 = 9
\]

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

6. **Solve for \( x \) by isolating it:**
\[
x + 1 = 3 \quad \text{or} \quad x + 1 = -3
\]
\[
x = 3 - 1 \quad \text{or} \quad x = -3 - 1
\]
\[
x = 2 \quad \text{or} \quad x = -4
\]

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