Question

Complete the square to solve the quadratic equation.
xsquaredplus2xminus12equals0

Answer 1

To solve the quadratic equation \( x^2 + 2x - 12 = 0 \) by completing the square, follow these steps:

1. **Move the constant term to the other side of the equation:**

\[
x^2 + 2x = 12
\]

2. **Find the coefficient of \( x \) (which is 2), divide it by 2, and then square it:**

\[
\left(\frac{2}{2}\right)^2 = 1
\]

3. **Add this square to both sides of the equation:**

\[
x^2 + 2x + 1 = 12 + 1
\]

This simplifies to:

\[
x^2 + 2x + 1 = 13
\]

4. **Recognize the left side as a perfect square:**

\[
(x + 1)^2 = 13
\]

5. **Take the square root of both sides:**

\[
x + 1 = \pm \sqrt{13}
\]

6. **Solve for \( x \):**

\[
x = -1 \pm \sqrt{13}
\]

Thus, the solutions to the equation \( x^2 + 2x - 12 = 0 \) are:

\[
x = -1 + \sqrt{13} \quad \text{and} \quad x = -1 - \sqrt{13}
\]