To complete the square for the expression \( x^2 + 2x \), follow these steps:

1. Start with the given expression:
   \[
   x^2 + 2x
   \]

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

3. Add and subtract this value (1) inside the expression:
   \[
   x^2 + 2x + 1 - 1
   \]

4. Now, rewrite the expression as a perfect square:
   \[
   (x + 1)^2 - 1
   \]

So, the completed square form of \( x^2 + 2x \) is:
\[
(x + 1)^2 - 1
\]

Would you like more details on this? Here are some related questions:

1. How do you complete the square for a quadratic with a non-unit leading coefficient?
2. What is the geometric interpretation of completing the square?
3. How does completing the square relate to solving quadratic equations?
4. Can completing the square be used to derive the quadratic formula?
5. How is completing the square applied in calculus for integration?

**Tip:** Completing the square is a powerful tool for transforming a quadratic expression into a form that reveals its vertex, which is useful in graphing and solving equations.

Learn how to complete the square for the quadratic expression x^2 + 2x. Follow the detailed step-by-step process to transform this expression into a perfect square form. Suitable for students in Grades 8-10, this tutorial covers key concepts in algebra and quadratic equations.

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