$$(7x^3-9x^2)^2 = 0$$
Answer
$$ \begin{matrix}x_1 = 0 & x_2 = \dfrac{ 9 }{ 7 } \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} (7x^3-9x^2)^2 &= 0&& \text{simplify left side} \\[1 em]49x^6-126x^5+81x^4 &= 0&& \\[1 em] \end{aligned} $$
In order to solve $ \color{blue}{ 49x^{6}-126x^{5}+81x^{4} = 0 } $, first we need to factor our $ x^4 $.
$$ 49x^{6}-126x^{5}+81x^{4} = x^4 \left( 49x^{2}-126x+81 \right) $$$ x = 0 $ is a root of multiplicity $ 4 $.
The remaining roots can be found by solving equation $ 49x^{2}-126x+81 = 0$.
$ 49x^{2}-126x+81 = 0 $ is a quadratic equation.
You can use step-by-step quadratic equation solver to see a detailed explanation on how to solve this equation.
This page was created using
Polynomial Equations Solver