0.3528x**3+3395.7x−35055=0

asked by guest
on Oct 20, 2024 at 10:03 pm



You asked:

Solve the equation \(0.3528 \cdot {x}^{3} + 3395.7 x - 35055 = 0\) for the variable \(x\).

MathBot Answer:

The 3 solutions to the equation are: \[\begin{aligned}x &= 5 \sqrt[3]{\frac{19475}{49} + \frac{10 \sqrt{4417722255}}{441}} - \frac{1925}{3 \sqrt[3]{\frac{19475}{49} + \frac{10 \sqrt{4417722255}}{441}}} \approx 10.212683\\x &= - \frac{5 \sqrt[3]{\frac{19475}{49} + \frac{10 \sqrt{4417722255}}{441}}}{2} + \frac{1925}{6 \sqrt[3]{\frac{19475}{49} + \frac{10 \sqrt{4417722255}}{441}}} + i \left(\frac{1925 \sqrt{3}}{6 \sqrt[3]{\frac{19475}{49} + \frac{10 \sqrt{4417722255}}{441}}} + \frac{5 \sqrt{3} \sqrt[3]{\frac{19475}{49} + \frac{10 \sqrt{4417722255}}{441}}}{2}\right) \approx -5.1063415 + 98.504945 i\\x &= - \frac{5 \sqrt[3]{\frac{19475}{49} + \frac{10 \sqrt{4417722255}}{441}}}{2} + \frac{1925}{6 \sqrt[3]{\frac{19475}{49} + \frac{10 \sqrt{4417722255}}{441}}} + i \left(- \frac{5 \sqrt{3} \sqrt[3]{\frac{19475}{49} + \frac{10 \sqrt{4417722255}}{441}}}{2} - \frac{1925 \sqrt{3}}{6 \sqrt[3]{\frac{19475}{49} + \frac{10 \sqrt{4417722255}}{441}}}\right) \approx -5.1063415 -98.504945 i\end{aligned}\]

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

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