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:
\[ x = \pm \sqrt{121} \]
Calculating the square root:
\[ \sqrt{121} = 11 \]
So the solutions are:
\[ x = 11 \quad \text{and} \quad x = -11 \]
Since the problem asks for the lesser number first, we write the solutions as:
\[ x = -11, \quad x = 11 \]
Thus, the answers are:
x = -11, x = 11