$$x^6+100x^2+\frac{44}{10}x^2-100 = 0$$
Answer
$$ \begin{matrix}x_1 = 0.9745 & x_2 = -0.9745 & x_3 = -2.21211+2.31695i \\[1 em] x_4 = -2.21211-2.31695i & x_5 = 2.21211+2.31695i & x_6 = 2.21211-2.31695i \end{matrix} $$
Explanation
$$ \begin{aligned} x^6+100x^2+\frac{44}{10}x^2-100 &= 0&& \text{multiply ALL terms by } \color{blue}{ 10 }. \\[1 em]10x^6+10\cdot100x^2+10 \cdot \frac{44}{10}x^2-10\cdot100 &= 10\cdot0&& \text{cancel out the denominators} \\[1 em]10x^6+1000x^2+44x^2-1000 &= 0&& \text{simplify left side} \\[1 em]10x^6+1044x^2-1000 &= 0&& \\[1 em] \end{aligned} $$
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using Newton method.
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