50x^3 + 149x^2 + 147x + 7 = 0

asked by guest
on Oct 08, 2024 at 7:24 pm



You asked:

Solve the equation \(50 \cdot {x}^{3} + 149 \cdot {x}^{2} + 147 x + 7 = 0\) for the variable \(x\).

MathBot Answer:

The 3 solutions to the equation are: \[\begin{aligned}x &= - \frac{149}{150} + \sqrt[3]{\frac{172997}{421875} + \frac{\sqrt{340513089}}{45000}} + \frac{151}{22500 \sqrt[3]{\frac{172997}{421875} + \frac{\sqrt{340513089}}{45000}}} \approx -0.050122681\\x &= - \frac{149}{150} - \frac{\sqrt[3]{\frac{\sqrt{340513089}}{45000} + \frac{172997}{421875}}}{2} - \frac{151}{45000 \sqrt[3]{\frac{\sqrt{340513089}}{45000} + \frac{172997}{421875}}} + i \left(- \frac{151 \sqrt{3}}{45000 \sqrt[3]{\frac{\sqrt{340513089}}{45000} + \frac{172997}{421875}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{340513089}}{45000} + \frac{172997}{421875}}}{2}\right) \approx -1.4649387 + 0.80442614 i\\x &= - \frac{149}{150} - \frac{\sqrt[3]{\frac{\sqrt{340513089}}{45000} + \frac{172997}{421875}}}{2} - \frac{151}{45000 \sqrt[3]{\frac{\sqrt{340513089}}{45000} + \frac{172997}{421875}}} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{340513089}}{45000} + \frac{172997}{421875}}}{2} + \frac{151 \sqrt{3}}{45000 \sqrt[3]{\frac{\sqrt{340513089}}{45000} + \frac{172997}{421875}}}\right) \approx -1.4649387 -0.80442614 i\end{aligned}\]

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

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