1. **State the problem:** Solve the quadratic equation $$x^2 + 16 = 0$$ for $x$. 2. **Formula and rules:** To solve equations of the form $$x^2 + c = 0$$, isolate $x^2$ and then take the square root of both sides. Remember that $$\sqrt{-a} = i\sqrt{a}$$ for $a > 0$, where $i$ is the imaginary unit. 3. **Isolate $x^2$:** $$x^2 = -16$$ 4. **Take the square root of both sides:** $$x = \pm \sqrt{-16}$$ 5. **Simplify the square root:** $$x = \pm \sqrt{-1 \times 16} = \pm \sqrt{-1} \times \sqrt{16} = \pm 4i$$ 6. **Final answer:** $$x = \pm 4i$$