Question

Complete the square to solve the quadratic equation.
xsquared2plus+2xminus−1212equals=0
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Question content area right
Part 1
xequals= enter your response here
​(Simplify your answer. Type an exact​ answer, using radicals as needed. Use a comma to separate answers as needed. ​)

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 right side of the equation**:
\[
x^2 + 2x = 12
\]

2. **Complete the square**:
- Take half of the coefficient of \( x \) (which is 2), square it, and add it to both sides of the equation.
- Half of 2 is 1, and squaring it gives 1.

So we add 1 to both sides:
\[
x^2 + 2x + 1 = 12 + 1
\]
This simplifies to:
\[
(x + 1)^2 = 13
\]

3. **Take the square root of both sides**:
\[
x + 1 = \pm \sqrt{13}
\]

4. **Solve for \( x \)**:
\[
x = -1 \pm \sqrt{13}
\]

This results in two solutions:
\[
x = -1 + \sqrt{13}, \quad x = -1 - \sqrt{13}
\]

So, the final answer can be written as:
\[
x = -1 + \sqrt{13}, -1 - \sqrt{13}
\]

You can type:
\[
-1 + \sqrt{13}, -1 - \sqrt{13}
\] as your response.