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# Algebra

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What is the sum of all real values of x that satisfy the equation (x-3)(x^2-x+4)=x-3+11?

Apr 16, 2022

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According to Wolfram Alpha, the only real value that satisfies this equation is $$x = \dfrac13 \left(4 - \dfrac{\sqrt[3]{4}}{\sqrt[3]{113+3\sqrt{1419}}} + \sqrt[3]{2\left(113+3\sqrt{1419}\right)}\right)$$.

Apr 16, 2022

According to Wolfram Alpha, the only real value that satisfies this equation is $$x = \dfrac13 \left(4 - \dfrac{\sqrt[3]{4}}{\sqrt[3]{113+3\sqrt{1419}}} + \sqrt[3]{2\left(113+3\sqrt{1419}\right)}\right)$$.