1. **State the problem:** Find the two values of $x$ such that $$x^2 - 14 = 50$$. 2. **Add 14 to both sides to isolate $x^2$:** $$x^2 - 14 + 14 = 50 + 14$$ $$x^2 = 64$$ 3. **Take the square root of both sides:** $$\sqrt{x^2} = \sqrt{64}$$ $$|x| = 8$$ 4. **Solve for $x$:** Since $|x| = 8$, then $$x = 8 \quad \text{or} \quad x = -8$$ 5. **Final answer:** The two values of $x$ are $8$ and $-8$.