To solve the equation \( x^2 + x = 0 \), we can factor it:

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

Now, set each factor equal to zero:

1. \( x = 0 \)
2. \( x + 1 = 0 \implies x = -1 \)

Thus, the solutions are \( x = 0 \) and \( x = -1 \).

Would you like more details or explanations about this process?

Here are five related questions:
1. How do you solve quadratic equations using the quadratic formula?
2. What is factoring, and why is it useful in solving equations?
3. How can you graph the function \( y = x^2 + x \)?
4. What does the solution of this equation represent geometrically?
5. How do you solve equations that cannot be factored easily?

**Tip:** Always check if a quadratic equation can be factored before using other methods like the quadratic formula or completing the square.

Learn how to solve the quadratic equation x² + x = 0 by factoring. This solution explains how to apply the factoring method and the Zero Product Property. Ideal for students in Grades 8-10.

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