1. **State the problem:** Solve the quadratic equation $$x^2 = 9x$$. 2. **Rewrite the equation:** Move all terms to one side to set the equation to zero: $$x^2 - 9x = 0$$ 3. **Factor the equation:** Factor out the common term $x$: $$x(x - 9) = 0$$ 4. **Apply the zero product property:** For the product to be zero, either factor must be zero: - $x = 0$ - $x - 9 = 0 \Rightarrow x = 9$ 5. **Final answer:** The solutions to the equation are: $$x = 0 \text{ or } x = 9$$ This means the values of $x$ that satisfy the original equation are 0 and 9.