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$$8372 \cdot \frac{x^5}{100}-22631\frac{x^4}{100}+22962\frac{x^3}{100}-10379\frac{x^2}{100}+17761\frac{x}{1000}-\frac{16}{10000} = 0$$
Answer
$$ \begin{matrix}x_1 = 9.0E-5 & x_2 = 0.54645+0.14599i & x_3 = 0.54645-0.14599i \\[1 em] x_4 = 0.80509+0.12082i & x_5 = 0.80509-0.12082i \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} 8372 \cdot \frac{x^5}{100}-22631\frac{x^4}{100}+22962\frac{x^3}{100}-10379\frac{x^2}{100}+17761\frac{x}{1000}-\frac{16}{10000} &= 0&& \text{multiply ALL terms by } \color{blue}{ 10000 }. \\[1 em]10000\cdot8372 \cdot \frac{x^5}{100}-10000\cdot22631\frac{x^4}{100}+10000\cdot22962\frac{x^3}{100}-10000\cdot10379\frac{x^2}{100}+10000\cdot17761\frac{x}{1000}-10000\cdot\frac{16}{10000} &= 10000\cdot0&& \text{cancel out the denominators} \\[1 em]837200x^5-2263100x^4+2296200x^3-1037900x^2+177610x-16 &= 0&& \\[1 em] \end{aligned} $$
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