  According to the Abel-Ruffini theorem [1] and Galois theory [2], there is no
solution in finite radicals to the general quintic equation. This article takes
a different approach and proposes a new method to solve the quintic by
iteration of radicals. But, the most intriguing result is an accurate algebraic
formula for absolute and relative root approximation: |formula - root| <
0.00432 and |formula/root - 1| < 0.0251. We then expand some of the geometric
properties discussed to construct a trigonometric algorithm that derives all
roots.
