1. **State the problem:** Solve the quadratic equation $x^2 + 7x = 0$ and find its roots. 2. **Formula and rules:** To solve a quadratic equation of the form $ax^2 + bx + c = 0$, we can factorize or use the quadratic formula. Here, $a=1$, $b=7$, and $c=0$. 3. **Factorization:** $$x^2 + 7x = x(x + 7) = 0$$ 4. **Apply zero product property:** For the product to be zero, either factor must be zero: $$x = 0 \quad \text{or} \quad x + 7 = 0$$ 5. **Solve each equation:** $$x = 0$$ $$x = -7$$ 6. **Final answer:** The roots of the equation are $\boxed{0 \text{ and } -7}$. These are the points where the graph of $y = x^2 + 7x$ crosses the x-axis.