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: \[ \boxed{2} \quad \text{and} \quad \boxed{-4} \]