Question
$$(x-2)^3 = 24$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} (x-2)^3 &= 24&& \text{simplify left side} \\[1 em]x^3-6x^2+12x-8 &= 24&& \text{move all terms to the left hand side } \\[1 em]x^3-6x^2+12x-8-24 &= 0&& \text{simplify left side} \\[1 em]x^3-6x^2+12x-32 &= 0&& \\[1 em] \end{aligned} $$
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