AHSME 1979 Problem 19

Find the sum of the squares of all real numbers satisfying the equation $x^{256}-256^{32}=0$. $\textbf{(A) }8 \textbf{(B) }128 \textbf{(C) }512 \textbf{(D) }65,536 \textbf{(E) }2(256^{32})$