250$x^{3}$+375$x^{2}$+3125$x$+1500=140000000

$x$=?

asked by guest
on Nov 14, 2024 at 1:47 am



You asked:

Solve the equation \(250 \cdot {x}^{3} + 375 \cdot {x}^{2} + 3125 x + 1500 = 140000000\) for the variable \(x\).

MathBot Answer:

The 3 solutions to the equation are: \[\begin{aligned}x &= - \frac{1}{2} + 5 \sqrt[3]{2240 + \frac{\sqrt{406425600311469}}{9000}} - \frac{47}{60 \sqrt[3]{2240 + \frac{\sqrt{406425600311469}}{9000}}} \approx 81.878188\\x &= - \frac{5 \sqrt[3]{2240 + \frac{\sqrt{406425600311469}}{9000}}}{2} - \frac{1}{2} + \frac{47}{120 \sqrt[3]{2240 + \frac{\sqrt{406425600311469}}{9000}}} + i \left(\frac{47 \sqrt{3}}{120 \sqrt[3]{2240 + \frac{\sqrt{406425600311469}}{9000}}} + \frac{5 \sqrt{3} \sqrt[3]{2240 + \frac{\sqrt{406425600311469}}{9000}}}{2}\right) \approx -41.689094 + 71.423907 i\\x &= - \frac{5 \sqrt[3]{2240 + \frac{\sqrt{406425600311469}}{9000}}}{2} - \frac{1}{2} + \frac{47}{120 \sqrt[3]{2240 + \frac{\sqrt{406425600311469}}{9000}}} + i \left(- \frac{5 \sqrt{3} \sqrt[3]{2240 + \frac{\sqrt{406425600311469}}{9000}}}{2} - \frac{47 \sqrt{3}}{120 \sqrt[3]{2240 + \frac{\sqrt{406425600311469}}{9000}}}\right) \approx -41.689094 -71.423907 i\end{aligned}\]

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

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