2016 AMC 10B Problem 1

The expression is equivalent to $$2a^{-2}+\frac{a^{-2}}{2} = 2.5 (a^{-1})^2.$$ Then $a^{-1}$ is equal to $\dfrac{1}{\frac 12} = 2,$ so our expression is equal to $2.5\cdot 2^2 = 10.$ Thus, the correct answer is D .