$$8372 \cdot \frac{x^5}{100}-22631\frac{x^4}{100}+22962\frac{x^3}{100}-10379\frac{x^2}{100}+18760\frac{x}{1000}-\frac{16}{10} = 0$$
Answer
$$ \begin{matrix}x_1 = 0.96465 & x_2 = 0.12679+0.11827i & x_3 = 0.12679-0.11827i \\[1 em] x_4 = 0.74247+0.32828i & x_5 = 0.74247-0.32828i \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} 8372 \cdot \frac{x^5}{100}-22631\frac{x^4}{100}+22962\frac{x^3}{100}-10379\frac{x^2}{100}+18760\frac{x}{1000}-\frac{16}{10} &= 0&& \text{multiply ALL terms by } \color{blue}{ 1000 }. \\[1 em]1000\cdot8372 \cdot \frac{x^5}{100}-1000\cdot22631\frac{x^4}{100}+1000\cdot22962\frac{x^3}{100}-1000\cdot10379\frac{x^2}{100}+1000\cdot18760\frac{x}{1000}-1000\cdot\frac{16}{10} &= 1000\cdot0&& \text{cancel out the denominators} \\[1 em]83720x^5-226310x^4+229620x^3-103790x^2+18760x-1600 &= 0&& \\[1 em] \end{aligned} $$
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using Newton method.
This page was created using
Polynomial Equations Solver