Isolate $x$ on finite geometric sum

Question

How can I isolate $x$ in terms of $n$, considering the following restriction?

$$1 = x + x^2 + x^3 + x^4 + … + x^n$$

For example $f(n=3) = 0.544$

Other hints:

• Only positive values of $x$ are accepted
• Approximated results are also valid

Answer 1

Polynomial equations of this type have no closed-form expression for $n>4$.