1. **State the problem:** Solve the quadratic equation $$x^2 = 49$$ for $$x$$. 2. **Formula and rules:** To solve $$x^2 = a$$, we take the square root of both sides, remembering that $$x$$ can be positive or negative. So, $$x = \pm \sqrt{a}$$. 3. **Apply the formula:** Here, $$a = 49$$. $$x = \pm \sqrt{49}$$ 4. **Simplify:** $$\sqrt{49} = 7$$. So, $$x = \pm 7$$. 5. **Interpretation:** This means $$x$$ can be either $$7$$ or $$-7$$. **Final answer:** $$\boxed{\pm 7}$$ corresponds to option C.