Question
$$(x+2)^2+(x+1)^3 = 0$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} (x+2)^2+(x+1)^3 &= 0&& \text{simplify left side} \\[1 em]x^2+4x+4+x^3+3x^2+3x+1 &= 0&& \\[1 em]x^3+4x^2+7x+5 &= 0&& \\[1 em] \end{aligned} $$
This polynomial has no rational roots that can be found using Rational Root Test.
Roots were found using qubic formulas.
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Equations Solver