Solve For A 8C85Da

1. **State the problem:** We need to solve for $a$ in the equation $$5 = a(-2 - \sqrt{5})(-2 + \sqrt{5}).$$ 2. **Recall the formula:** The product of conjugates $$(x - y)(x + y) = x^2 - y^2.$$ Here, $x = -2$ and $y = \sqrt{5}$. 3. **Apply the formula:** $$(-2 - \sqrt{5})(-2 + \sqrt{5}) = (-2)^2 - (\sqrt{5})^2 = 4 - 5 = -1.$$ 4. **Substitute back:** $$5 = a \times (-1)$$ 5. **Solve for $a$:** $$5 = -a$$ 6. **Isolate $a$:** $$a = \cancel{-1} \times \frac{5}{\cancel{-1}} = -5.$$ **Final answer:** $$a = -5.$$