To solve the equation \( x^2 - 121 = 0 \), we can first add 121 to both sides:
\[ x^2 = 121 \]
Next, take the square root of both sides:
\[ x = \pm 11 \]
Thus, the solutions are:
\[ x = -11 \quad \text{and} \quad x = 11 \]
When entering the solutions with the lesser number first, the answer is:
\[ x = -11, \quad x = 11 \]