$$10000 = \frac{253}{100}x^5-\frac{5765}{100}x^4+\frac{50561}{100}x^3-\frac{18762}{10}x^2+\frac{29192}{10}x+\frac{36396}{10}$$
Answer
$$ \begin{matrix}x_1 = 7.14266 & x_2 = 0.27648+2.14753i & x_3 = 0.27648-2.14753i \\[1 em] x_4 = 7.54547+4.25906i & x_5 = 7.54547-4.25906i \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} 10000 &= \frac{253}{100}x^5-\frac{5765}{100}x^4+\frac{50561}{100}x^3-\frac{18762}{10}x^2+\frac{29192}{10}x+\frac{36396}{10}&& \text{multiply ALL terms by } \color{blue}{ 100 }. \\[1 em]100\cdot10000 &= 100 \cdot \frac{253}{100}x^5-100\frac{5765}{100}x^4+100\frac{50561}{100}x^3-100\frac{18762}{10}x^2+100\frac{29192}{10}x+100\cdot\frac{36396}{10}&& \text{cancel out the denominators} \\[1 em]1000000 &= 253x^5-5765x^4+50561x^3-187620x^2+291920x+363960&& \text{move all terms to the left hand side } \\[1 em]1000000-253x^5+5765x^4-50561x^3+187620x^2-291920x-363960 &= 0&& \text{simplify left side} \\[1 em]-253x^5+5765x^4-50561x^3+187620x^2-291920x+636040 &= 0&& \\[1 em] \end{aligned} $$
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