To solve the equation \( x^2 - 121 = 0 \), we can first rewrite it by isolating \( x^2 \):
\[ x^2 = 121 \]
Next, we take the square root of both sides. Remember that taking the square root results in two possible solutions (the positive and negative roots):
\[ x = \pm \sqrt{121} \]
Calculating the square root gives us:
\[ \sqrt{121} = 11 \]
Therefore, the two solutions are:
\[ x = 11 \quad \text{and} \quad x = -11 \]
In conclusion, the solutions to the equation \( x^2 - 121 = 0 \) are:
\[ x = 11 \quad \text{and} \quad x = -11 \]