Question
$$(x^2+2x)^2 = x^4+3+4x$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} (x^2+2x)^2 &= x^4+3+4x&& \text{simplify left and right hand side} \\[1 em]x^4+4x^3+4x^2 &= x^4+4x+3&& \text{move all terms to the left hand side } \\[1 em]x^4+4x^3+4x^2-x^4-4x-3 &= 0&& \text{simplify left side} \\[1 em]x^4+4x^3+4x^2-x^4-4x-3 &= 0&& \\[1 em]4x^3+4x^2-4x-3 &= 0&& \\[1 em] \end{aligned} $$
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