Question

Complete the square to solve the following quadratic equation: x^2 + 2x − 8 = 0.
A) x = 10, x = -8
B) x = 2, x = -4
C) x = -2, x = 4
D) x = -10, x = 8

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:
\[
x^2 + 2x = 8
\]

2. Identify the coefficient of \( x \), which is 2. Take half of it and square the result:
\[
\left( \frac{2}{2} \right)^2 = 1
\]

3. Add this square to both sides of the equation:
\[
x^2 + 2x + 1 = 8 + 1
\]
This simplifies to:
\[
(x + 1)^2 = 9
\]

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 are \( x = 2 \) and \( x = -4 \).

The correct option is **B) x = 2, x = -4**.