Summation+nested radical

Calculus Level 3

If n=1n22n=S\displaystyle \sum_{n=1}^\infty \frac{ n^2 } { 2^n } = S ,
and f(x)=x+x+x+x+ f(x) = \sqrt{ x + \sqrt{ x + \sqrt{ x + \sqrt{ x + \ldots}}}} ,
find f(S) f(S) .

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