0.19t³ + 13t + 40 - 400 = 0

asked by guest
on Apr 02, 2025 at 5:33 pm



You asked:

Solve the equation 0.19t3+13t+40−400=00.19 {t}^{3} + 13 t + 40 - 400 = 0 for the variable tt.

MathBot Answer:

The 3 solutions to the equation are: t=101819+959931332493−130571819+959931332493≈10.546652t=−51819+959931332493+65571819+959931332493+i(653571819+959931332493+531819+959931332493)≈−5.273326+12.322538it=−51819+959931332493+65571819+959931332493+i(−531819+959931332493−653571819+959931332493)≈−5.273326−12.322538i\begin{aligned}t &= 10 \sqrt[3]{\frac{18}{19} + \frac{\sqrt{9599313}}{3249}} - \frac{130}{57 \sqrt[3]{\frac{18}{19} + \frac{\sqrt{9599313}}{3249}}} \approx 10.546652\\t &= - 5 \sqrt[3]{\frac{18}{19} + \frac{\sqrt{9599313}}{3249}} + \frac{65}{57 \sqrt[3]{\frac{18}{19} + \frac{\sqrt{9599313}}{3249}}} + i \left(\frac{65 \sqrt{3}}{57 \sqrt[3]{\frac{18}{19} + \frac{\sqrt{9599313}}{3249}}} + 5 \sqrt{3} \sqrt[3]{\frac{18}{19} + \frac{\sqrt{9599313}}{3249}}\right) \approx -5.273326 + 12.322538 i\\t &= - 5 \sqrt[3]{\frac{18}{19} + \frac{\sqrt{9599313}}{3249}} + \frac{65}{57 \sqrt[3]{\frac{18}{19} + \frac{\sqrt{9599313}}{3249}}} + i \left(- 5 \sqrt{3} \sqrt[3]{\frac{18}{19} + \frac{\sqrt{9599313}}{3249}} - \frac{65 \sqrt{3}}{57 \sqrt[3]{\frac{18}{19} + \frac{\sqrt{9599313}}{3249}}}\right) \approx -5.273326 -12.322538 i\end{aligned}

ii is the imaginary unit, defined as i2=−1i^2 = -1.

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