Question
$$5x^4-4x^4x^5 = 0$$
Answer
$$ x = 0 $$
Explanation
$$ \begin{aligned} 5x^4-4x^4x^5 &= 0&& \text{simplify left side} \\[1 em]5x^4-4x^9 &= 0&& \\[1 em]-4x^9+5x^4 &= 0&& \\[1 em] \end{aligned} $$
In order to solve $ \color{blue}{ -4x^{9}+5x^{4} = 0 } $, first we need to factor our $ x^4 $.
$$ -4x^{9}+5x^{4} = x^4 \left( -4x^{5}+5 \right) $$$ x = 0 $ is a root of multiplicity $ 4 $.
The remaining roots can be found by solving equation $ -4x^{5}+5 = 0$.
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