Question

Complete the square to solve the quadratic equation.
xsquaredplus2xminus2equals0

Answer 1

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

1. Start with the equation:
\[
x^2 + 2x - 2 = 0
\]

2. Move the constant term to the right side of the equation:
\[
x^2 + 2x = 2
\]

3. To complete the square, take half of the coefficient of \( x \) (which is 2), square it, and add it to both sides. Half of 2 is 1, and squaring it gives \( 1^2 = 1 \):
\[
x^2 + 2x + 1 = 2 + 1
\]

4. This simplifies to:
\[
(x + 1)^2 = 3
\]

5. Now, take the square root of both sides:
\[
x + 1 = \pm \sqrt{3}
\]

6. Solve for \( x \) by isolating it:
\[
x = -1 \pm \sqrt{3}
\]

Thus, the solutions to the equation \( x^2 + 2x - 2 = 0 \) are:
\[
x = -1 + \sqrt{3} \quad \text{and} \quad x = -1 - \sqrt{3}
\]