Let x, y, and z be real numbers satisfying the system of equations
\begin{aligned}
& x y+4 z=60 \\
& y z+4 x=60 \\
& z x+4 y=60
\end{aligned}
Let S be the set of possible values of x. Find the sum of the squares of the elements of S.
Let x, y, and z be real numbers satisfying the system of equations
Let S be the set of possible values of x. Find the sum of the squares of the elements of S.