1. State the problem: Solve the quadratic equation $$x^2 - 144 = 0$$. 2. Move constant term to the other side: $$x^2 = 144$$. 3. Take the square root of both sides, remembering to include both positive and negative roots: $$x = \pm \sqrt{144}$$. 4. Simplify the square root: $$x = \pm 12$$. 5. Therefore, the solutions are $$x = 12$$ and $$x = -12$$.