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!