1. The problem is to solve the equation $x^2 = 81$. 2. The formula used here is to take the square root of both sides to solve for $x$. Remember, when you take the square root of both sides, you must consider both the positive and negative roots. 3. Taking the square root of both sides gives: $$x = \pm \sqrt{81}$$ 4. Since $\sqrt{81} = 9$, we have: $$x = \pm 9$$ 5. Therefore, the solutions are $x = 9$ and $x = -9$. 6. This means both 9 and -9, when squared, will give 81, satisfying the original equation.