# Inspired Infinite Equation

Algebra Level 3

$1= x^{2} - x^{3} + x^{4} -x^{5} +\ldots$Solve for $x$ in the equation above.

If the sum of all values of $x$ can be represented in the form $\dfrac{a+b\sqrt{c}}{d}$, such that $a,b,c$ and $d$ are integers and the fraction is in lowest form and $d> 0$, find $a+b+c+d$.

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