To solve the equation \( x^2 - 121 = 0 \), we can start by isolating \( x^2 \):
\[ x^2 = 121 \]
Next, we take the square root of both sides:
\[ x = \pm \sqrt{121} \]
Since \( \sqrt{121} = 11 \), we have:
\[ x = 11 \quad \text{or} \quad x = -11 \]
Thus, the solutions to the equation \( x^2 - 121 = 0 \) are \( -11 \) and \( 11 \).
In the required format, entering the lesser number first, the solutions are:
\[ -11, 11 \]