1. **State the problem:** Solve the quadratic equation $x^2 + 8x + 16 = 0$ using the discriminant formula $D = b^2 - 4ac$. 2. **Identify coefficients:** Here, $a = 1$, $b = 8$, and $c = 16$. 3. **Calculate the discriminant:** $$D = b^2 - 4ac = 8^2 - 4 \times 1 \times 16 = 64 - 64 = 0$$ 4. **Interpret the discriminant:** Since $D = 0$, the quadratic has exactly one real root (a repeated root). 5. **Use the quadratic formula:** $$x = \frac{-b \pm \sqrt{D}}{2a} = \frac{-8 \pm \sqrt{0}}{2 \times 1} = \frac{-8 \pm 0}{2}$$ 6. **Simplify the expression:** $$x = \frac{\cancel{-8} \pm 0}{\cancel{2}} = -4$$ 7. **Final answer:** The solution to the equation is $x = -4$.