1. **State the problem:** Solve the quadratic equation $x^2 = 81$. 2. **Formula and rules:** To solve $x^2 = a$, we take the square root of both sides, remembering that both positive and negative roots are possible. So, $x = \pm \sqrt{a}$. 3. **Apply the formula:** Here, $a = 81$, so $$x = \pm \sqrt{81}$$ 4. **Calculate the square root:** $$x = \pm 9$$ 5. **Final answer:** The solutions to the equation $x^2 = 81$ are $$x = 9 \text{ or } x = -9$$ This means both 9 and -9, when squared, give 81.