1. **State the problem:** Solve the equation $$x^2 - 49 = 0$$ by square rooting. 2. **Rewrite the equation:** Add 49 to both sides to isolate the squared term: $$x^2 - 49 + 49 = 0 + 49$$ $$x^2 = 49$$ 3. **Apply the square root property:** Taking the square root of both sides gives: $$\sqrt{x^2} = \pm \sqrt{49}$$ $$|x| = \pm 7$$ 4. **Simplify absolute value:** This means: $$x = 7 \quad \text{or} \quad x = -7$$ 5. **Final answer:** The solutions to the equation are $$x = 7$$ and $$x = -7$$.