To solve the equation \( x^2 = 144 \), we will take the square root of both sides. Remember that taking the square root of both sides results in two potential solutions (the positive and negative roots).
\[ x = \sqrt{144} \quad \text{or} \quad x = -\sqrt{144} \]
Calculating the square root:
\[ \sqrt{144} = 12 \]
Thus, we have:
\[ x = 12 \quad \text{or} \quad x = -12 \]
The solutions for the equation \( x^2 = 144 \) are:
\[ x = 12 \quad \text{and} \quad x = -12 \]