1. **State the problem:** Solve the quadratic equation $x^2 + 5x - 50 = 0$ using the discriminant formula $D = b^2 - 4ac$. 2. **Identify coefficients:** Here, $a = 1$, $b = 5$, and $c = -50$. 3. **Calculate the discriminant:** $$D = b^2 - 4ac = 5^2 - 4 \times 1 \times (-50) = 25 + 200 = 225$$ 4. **Interpret the discriminant:** Since $D > 0$, there are two distinct real roots. 5. **Use the quadratic formula:** $$x = \frac{-b \pm \sqrt{D}}{2a} = \frac{-5 \pm \sqrt{225}}{2 \times 1} = \frac{-5 \pm 15}{2}$$ 6. **Find the two solutions:** - For the plus sign: $$x = \frac{-5 + 15}{2} = \frac{10}{2} = 5$$ - For the minus sign: $$x = \frac{-5 - 15}{2} = \frac{-20}{2} = -10$$ **Final answer:** The solutions are $x = 5$ and $x = -10$.