1. **State the problem:** Solve for $a$ in the equation $0 = a(5 - 2.5)^2 + 10$. 2. **Simplify inside the parentheses:** Calculate $5 - 2.5$. $$5 - 2.5 = 2.5$$ 3. **Square the result:** Calculate $(2.5)^2$. $$2.5^2 = 6.25$$ 4. **Rewrite the equation:** Substitute back into the equation. $$0 = a \times 6.25 + 10$$ 5. **Isolate the term with $a$:** Subtract 10 from both sides. $$0 - 10 = a \times 6.25 + 10 - 10$$ $$-10 = a \times 6.25$$ 6. **Solve for $a$:** Divide both sides by 6.25. $$a = \frac{-10}{6.25}$$ 7. **Simplify the fraction:** $$a = -\frac{10}{6.25} = -\frac{10 \times \cancel{4}}{6.25 \times \cancel{4}} = -\frac{40}{25}$$ $$a = -\frac{40}{25} = -\frac{8}{5} = -1.6$$ **Final answer:** $$a = -1.6$$