x(x*x-11x+10)=-200

asked by guest
on Jan 24, 2025 at 3:16 pm



You asked:

Solve the equation \(x\left( x \cdot x - 11 x + 10 \right) = -200\) for the variable \(x\).

MathBot Answer:

The 3 solutions to the equation are: \[\begin{aligned}x &= \frac{11}{3} - \frac{91}{3 \sqrt[3]{1864 + 15 \sqrt{12093}}} - \frac{\sqrt[3]{1864 + 15 \sqrt{12093}}}{3} \approx -3.3961138\\x &= \frac{91}{6 \sqrt[3]{15 \sqrt{12093} + 1864}} + \frac{\sqrt[3]{15 \sqrt{12093} + 1864}}{6} + \frac{11}{3} + i \left(- \frac{91 \sqrt{3}}{6 \sqrt[3]{15 \sqrt{12093} + 1864}} + \frac{\sqrt{3} \sqrt[3]{15 \sqrt{12093} + 1864}}{6}\right) \approx 7.1980569 + 2.6606048 i\\x &= \frac{91}{6 \sqrt[3]{15 \sqrt{12093} + 1864}} + \frac{\sqrt[3]{15 \sqrt{12093} + 1864}}{6} + \frac{11}{3} + i \left(- \frac{\sqrt{3} \sqrt[3]{15 \sqrt{12093} + 1864}}{6} + \frac{91 \sqrt{3}}{6 \sqrt[3]{15 \sqrt{12093} + 1864}}\right) \approx 7.1980569 -2.6606048 i\end{aligned}\]

\(i\) is the imaginary unit, defined as \(i^2 = -1\).

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