The equation given is a quadratic equation:

\[
x^2 + 2x + 1 = 0
\]

This can be factored as:

\[
(x + 1)(x + 1) = 0
\]

So, the solution is:

\[
x + 1 = 0 \quad \Rightarrow \quad x = -1
\]

Thus, the only solution is \( x = -1 \).

Would you like more details on factoring quadratic equations or other methods like the quadratic formula?

Here are 5 related questions:
1. How do you factor different types of quadratic equations?
2. What is the quadratic formula, and how does it work?
3. Can a quadratic equation have complex solutions?
4. How can we graph a quadratic equation and interpret its solutions?
5. What are the sum and product of the roots of a quadratic equation?

**Tip:** Always check if a quadratic equation can be factored before using the quadratic formula—it often simplifies the process!

Learn how to solve the quadratic equation x^2 + 2x + 1 = 0 using factoring techniques. This problem covers essential algebraic concepts, such as the quadratic equation and the zero product property. Suitable for students in Grades 7-9.

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