To complete the square for the equation \( x^2 - 2x = 2 \), we'll follow these steps:

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

\[
x^2 - 2x = 2
\]

2. **Find the value needed to complete the square:**  
   Take half of the coefficient of \( x \) (which is \(-2\)), square it, and add it to both sides.

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

Add 1 to both sides:

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

3. **Rewrite the left side as a perfect square:**

\[
(x - 1)^2 = 3
\]

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

Take the square root of both sides:

\[
x - 1 = \pm \sqrt{3}
\]

Finally, solve for \( x \):

\[
x = 1 \pm \sqrt{3}
\]

### Solution:
The values of \( x \) are:

\[
x = 1 + \sqrt{3} \quad \text{or} \quad x = 1 - \sqrt{3}
\]

Would you like a more detailed explanation of this process or have any questions?

### Related Questions:

1. How do you solve quadratic equations by completing the square for different coefficients?
2. What are the other methods to solve a quadratic equation besides completing the square?
3. Can you use completing the square to find the vertex form of a quadratic equation?
4. How does completing the square help in understanding the properties of a parabola?
5. What is the geometric interpretation of completing the square?

**Tip:** Completing the square is useful for converting a quadratic equation into vertex form, which makes it easier to graph and analyze.

Learn how to solve the quadratic equation x² - 2x = 2 by completing the square. This step-by-step guide explains key algebraic concepts, including how to transform a quadratic equation into a perfect square trinomial. Perfect for students in Grades 9-10.

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