4.9x $x^{2}$+5x-10=0

asked by guest
on Nov 17, 2024 at 7:39 am



You asked:

Solve the equation \(4.9 x \cdot {x}^{2} + 5 x - 10 = 0\) for the variable \(x\).

MathBot Answer:

The 3 solutions to the equation are: \[\begin{aligned}x &= \sqrt[3]{\frac{50}{49} + \frac{50 \sqrt{4119}}{3087}} - \frac{50}{147 \sqrt[3]{\frac{50}{49} + \frac{50 \sqrt{4119}}{3087}}} \approx 1.005057\\x &= - \frac{\sqrt[3]{\frac{50}{49} + \frac{50 \sqrt{4119}}{3087}}}{2} + \frac{25}{147 \sqrt[3]{\frac{50}{49} + \frac{50 \sqrt{4119}}{3087}}} + i \left(\frac{25 \sqrt{3}}{147 \sqrt[3]{\frac{50}{49} + \frac{50 \sqrt{4119}}{3087}}} + \frac{\sqrt{3} \sqrt[3]{\frac{50}{49} + \frac{50 \sqrt{4119}}{3087}}}{2}\right) \approx -0.50252851 + 1.3334215 i\\x &= - \frac{\sqrt[3]{\frac{50}{49} + \frac{50 \sqrt{4119}}{3087}}}{2} + \frac{25}{147 \sqrt[3]{\frac{50}{49} + \frac{50 \sqrt{4119}}{3087}}} + i \left(- \frac{\sqrt{3} \sqrt[3]{\frac{50}{49} + \frac{50 \sqrt{4119}}{3087}}}{2} - \frac{25 \sqrt{3}}{147 \sqrt[3]{\frac{50}{49} + \frac{50 \sqrt{4119}}{3087}}}\right) \approx -0.50252851 -1.3334215 i\end{aligned}\]

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

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