1. **State the problem:** Solve the quadratic equation $$z^2 + 10z - 24 = 0$$ to find the values of $z$. 2. **Recall the quadratic formula:** For an equation $$az^2 + bz + c = 0$$, the solutions are given by $$z = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$ where $a=1$, $b=10$, and $c=-24$. 3. **Calculate the discriminant:** $$\Delta = b^2 - 4ac = 10^2 - 4 \times 1 \times (-24) = 100 + 96 = 196$$ 4. **Find the square root of the discriminant:** $$\sqrt{196} = 14$$ 5. **Apply the quadratic formula:** $$z = \frac{-10 \pm 14}{2 \times 1} = \frac{-10 \pm 14}{2}$$ 6. **Calculate the two solutions:** - For the plus sign: $$z = \frac{-10 + 14}{2} = \frac{4}{2} = 2$$ - For the minus sign: $$z = \frac{-10 - 14}{2} = \frac{-24}{2} = -12$$ 7. **Answer:** The two solutions are $$z = 2$$ and $$z = -12$$. One of the solutions is $$\boxed{2}$$.