298.386x ^ { 3 } +751.41x ^ { 2 } -882 = 0

asked by guest
on Jan 20, 2025 at 11:09 pm



You asked:

Solve the equation \(298.386 {x}^{3} + 751.41 {x}^{2} - 882 = 0\) for the variable \(x\).

MathBot Answer:

The 3 solutions to the equation are: \[\begin{aligned}x &= - \frac{115}{137} + 5 \sqrt[3]{\frac{2206517}{311133713} + \frac{42 \sqrt{81590}}{2271049}} + \frac{2645}{18769 \sqrt[3]{\frac{2206517}{311133713} + \frac{42 \sqrt{81590}}{2271049}}} \approx 0.92635128\\x &= - \frac{115}{137} - \frac{5 \sqrt[3]{\frac{42 \sqrt{81590}}{2271049} + \frac{2206517}{311133713}}}{2} - \frac{2645}{37538 \sqrt[3]{\frac{42 \sqrt{81590}}{2271049} + \frac{2206517}{311133713}}} + i \left(- \frac{2645 \sqrt{3}}{37538 \sqrt[3]{\frac{42 \sqrt{81590}}{2271049} + \frac{2206517}{311133713}}} + \frac{5 \sqrt{3} \sqrt[3]{\frac{42 \sqrt{81590}}{2271049} + \frac{2206517}{311133713}}}{2}\right) \approx -1.7222997 + 0.47391219 i\\x &= - \frac{115}{137} - \frac{5 \sqrt[3]{\frac{42 \sqrt{81590}}{2271049} + \frac{2206517}{311133713}}}{2} - \frac{2645}{37538 \sqrt[3]{\frac{42 \sqrt{81590}}{2271049} + \frac{2206517}{311133713}}} + i \left(- \frac{5 \sqrt{3} \sqrt[3]{\frac{42 \sqrt{81590}}{2271049} + \frac{2206517}{311133713}}}{2} + \frac{2645 \sqrt{3}}{37538 \sqrt[3]{\frac{42 \sqrt{81590}}{2271049} + \frac{2206517}{311133713}}}\right) \approx -1.7222997 -0.47391219 i\end{aligned}\]

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

+ Submit Question