519365.96$a^{3}$ = a+ 0.14

asked by guest
on Nov 16, 2024 at 3:07 pm



You asked:

Solve the equation \(519365.96 \cdot {a}^{3} = a + 0.14\) for the variable \(a\).

MathBot Answer:

The 3 solutions to the equation are: \[\begin{aligned}a &= \sqrt[3]{\frac{7}{51936596} + \frac{\sqrt{669116531022173769}}{6069172509151236}} + \frac{25}{38952447 \sqrt[3]{\frac{7}{51936596} + \frac{\sqrt{669116531022173769}}{6069172509151236}}} \approx 0.0065591335\\a &= - \frac{\sqrt[3]{\frac{\sqrt{669116531022173769}}{6069172509151236} + \frac{7}{51936596}}}{2} - \frac{25}{77904894 \sqrt[3]{\frac{\sqrt{669116531022173769}}{6069172509151236} + \frac{7}{51936596}}} + i \left(- \frac{25 \sqrt{3}}{77904894 \sqrt[3]{\frac{\sqrt{669116531022173769}}{6069172509151236} + \frac{7}{51936596}}} + \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{669116531022173769}}{6069172509151236} + \frac{7}{51936596}}}{2}\right) \approx -0.0032795667 + 0.0055082891 i\\a &= - \frac{\sqrt[3]{\frac{\sqrt{669116531022173769}}{6069172509151236} + \frac{7}{51936596}}}{2} - \frac{25}{77904894 \sqrt[3]{\frac{\sqrt{669116531022173769}}{6069172509151236} + \frac{7}{51936596}}} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{\sqrt{669116531022173769}}{6069172509151236} + \frac{7}{51936596}}}{2} + \frac{25 \sqrt{3}}{77904894 \sqrt[3]{\frac{\sqrt{669116531022173769}}{6069172509151236} + \frac{7}{51936596}}}\right) \approx -0.0032795667 -0.0055082891 i\end{aligned}\]

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

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