$$x(x+3)^2+(x-7)^4 = 0$$
Answer
$$ \begin{matrix}x_1 = 3.73199+1.91i & x_2 = 3.73199-1.91i & x_3 = 9.76801+6.41822i \\[1 em] x_4 = 9.76801-6.41822i & \\[1 em] \end{matrix} $$
Explanation
$$ \begin{aligned} x(x+3)^2+(x-7)^4 &= 0&& \text{simplify left side} \\[1 em]x(x^2+6x+9)+x^4-28x^3+294x^2-1372x+2401 &= 0&& \\[1 em]x^3+6x^2+9x+x^4-28x^3+294x^2-1372x+2401 &= 0&& \\[1 em]x^4-27x^3+300x^2-1363x+2401 &= 0&& \\[1 em] \end{aligned} $$
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using quartic formulas
This page was created using
Polynomial Equations Solver