1. **State the problem:** Simplify the expression $$\frac{-1\pm\sqrt{1-4+16}}{2}$$. 2. **Simplify inside the square root:** Calculate the value under the square root (discriminant). $$1 - 4 + 16 = 13$$ 3. **Rewrite the expression:** $$\frac{-1 \pm \sqrt{13}}{2}$$ 4. **Explain the meaning:** This expression represents two values because of the $\pm$ sign: one with plus and one with minus. 5. **Final simplified form:** $$x = \frac{-1 + \sqrt{13}}{2} \quad \text{or} \quad x = \frac{-1 - \sqrt{13}}{2}$$ These are the two solutions.