# Reverse Engineer This Transcendental Equation!

**Algebra**Level 5

Let \(a\) be any natural number, and let \(f(x)={ a }^{ 2 }{ x }^{ 2 }-x-{ 1 }\). Consider

\({ f(x) }^{ { f(x) }^{ f(x) } }= { 2015 }\).

If the sum of all solutions for \(x\) is \(k\), determine \(\frac { { \pi }^{ 2 } }{ k } \). (This means if for some value of \(x\) you can set a value of \(a\) such that it satisfies the equation, then that value of \(x\) is a solution)