1. The problem is to understand why the solutions to $x^2 = 81$ are both positive and negative 9. 2. The key formula is that if $x^2 = a$, then $x = \pm \sqrt{a}$, meaning both positive and negative roots. 3. This is because squaring a number always gives a positive result: $9^2 = 81$ and $(-9)^2 = 81$. 4. So, both $9$ and $-9$ satisfy the equation $x^2 = 81$. 5. Therefore, the solution includes both $x = 9$ and $x = -9$ to cover all possible values of $x$ that make the equation true.