(-60) + 28 / (x^1) + 28/ (x^2) + 28/ (x^3) + 28/ (x^4) = 0.00001

asked by guest
on Jan 07, 2025 at 3:01 am



You asked:

Solve the equation \(-60 + \frac{28}{{x}^{1}} + \frac{28}{{x}^{2}} + \frac{28}{{x}^{3}} + \frac{28}{{x}^{4}} = 0.00001\) for the variable \(x\).

MathBot Answer:

The complex solutions are: \[\left\{\frac{100000}{857143} + \frac{\sqrt{- \frac{2217143200000}{6612247102041 \sqrt[3]{- \frac{465714350000000000}{17002923953354186589} + \frac{80000000 \sqrt{27417497434877861835}}{5667641317784728863}}} + \frac{805714400000}{2204082367347} + 2 \sqrt[3]{- \frac{465714350000000000}{17002923953354186589} + \frac{80000000 \sqrt{27417497434877861835}}{5667641317784728863}}}}{2} + \frac{\sqrt{\left|{- 2 \sqrt[3]{- \frac{465714350000000000}{17002923953354186589} + \frac{80000000 \sqrt{27417497434877861835}}{5667641317784728863}} + \frac{1611428800000}{2204082367347} + \frac{2217143200000}{6612247102041 \sqrt[3]{- \frac{465714350000000000}{17002923953354186589} + \frac{80000000 \sqrt{27417497434877861835}}{5667641317784728863}}} + \frac{740898177959200000}{629737924198303207 \sqrt{- \frac{2217143200000}{6612247102041 \sqrt[3]{- \frac{465714350000000000}{17002923953354186589} + \frac{80000000 \sqrt{27417497434877861835}}{5667641317784728863}}} + \frac{805714400000}{2204082367347} + 2 \sqrt[3]{- \frac{465714350000000000}{17002923953354186589} + \frac{80000000 \sqrt{27417497434877861835}}{5667641317784728863}}}}}\right|}}{2}, - \frac{\sqrt{- \frac{2217143200000}{6612247102041 \sqrt[3]{- \frac{465714350000000000}{17002923953354186589} + \frac{80000000 \sqrt{27417497434877861835}}{5667641317784728863}}} + \frac{805714400000}{2204082367347} + 2 \sqrt[3]{- \frac{465714350000000000}{17002923953354186589} + \frac{80000000 \sqrt{27417497434877861835}}{5667641317784728863}}}}{2} + \frac{100000}{857143} - \frac{i \sqrt{\left|{- \frac{740898177959200000}{629737924198303207 \sqrt{- \frac{2217143200000}{6612247102041 \sqrt[3]{- \frac{465714350000000000}{17002923953354186589} + \frac{80000000 \sqrt{27417497434877861835}}{5667641317784728863}}} + \frac{805714400000}{2204082367347} + 2 \sqrt[3]{- \frac{465714350000000000}{17002923953354186589} + \frac{80000000 \sqrt{27417497434877861835}}{5667641317784728863}}}} - 2 \sqrt[3]{- \frac{465714350000000000}{17002923953354186589} + \frac{80000000 \sqrt{27417497434877861835}}{5667641317784728863}} + \frac{1611428800000}{2204082367347} + \frac{2217143200000}{6612247102041 \sqrt[3]{- \frac{465714350000000000}{17002923953354186589} + \frac{80000000 \sqrt{27417497434877861835}}{5667641317784728863}}}}\right|}}{2}, - \frac{\sqrt{- \frac{2217143200000}{6612247102041 \sqrt[3]{- \frac{465714350000000000}{17002923953354186589} + \frac{80000000 \sqrt{27417497434877861835}}{5667641317784728863}}} + \frac{805714400000}{2204082367347} + 2 \sqrt[3]{- \frac{465714350000000000}{17002923953354186589} + \frac{80000000 \sqrt{27417497434877861835}}{5667641317784728863}}}}{2} + \frac{100000}{857143} + \frac{i \sqrt{\left|{- \frac{740898177959200000}{629737924198303207 \sqrt{- \frac{2217143200000}{6612247102041 \sqrt[3]{- \frac{465714350000000000}{17002923953354186589} + \frac{80000000 \sqrt{27417497434877861835}}{5667641317784728863}}} + \frac{805714400000}{2204082367347} + 2 \sqrt[3]{- \frac{465714350000000000}{17002923953354186589} + \frac{80000000 \sqrt{27417497434877861835}}{5667641317784728863}}}} - 2 \sqrt[3]{- \frac{465714350000000000}{17002923953354186589} + \frac{80000000 \sqrt{27417497434877861835}}{5667641317784728863}} + \frac{1611428800000}{2204082367347} + \frac{2217143200000}{6612247102041 \sqrt[3]{- \frac{465714350000000000}{17002923953354186589} + \frac{80000000 \sqrt{27417497434877861835}}{5667641317784728863}}}}\right|}}{2}, - \frac{\sqrt{\left|{- 2 \sqrt[3]{- \frac{465714350000000000}{17002923953354186589} + \frac{80000000 \sqrt{27417497434877861835}}{5667641317784728863}} + \frac{1611428800000}{2204082367347} + \frac{2217143200000}{6612247102041 \sqrt[3]{- \frac{465714350000000000}{17002923953354186589} + \frac{80000000 \sqrt{27417497434877861835}}{5667641317784728863}}} + \frac{740898177959200000}{629737924198303207 \sqrt{- \frac{2217143200000}{6612247102041 \sqrt[3]{- \frac{465714350000000000}{17002923953354186589} + \frac{80000000 \sqrt{27417497434877861835}}{5667641317784728863}}} + \frac{805714400000}{2204082367347} + 2 \sqrt[3]{- \frac{465714350000000000}{17002923953354186589} + \frac{80000000 \sqrt{27417497434877861835}}{5667641317784728863}}}}}\right|}}{2} + \frac{100000}{857143} + \frac{\sqrt{- \frac{2217143200000}{6612247102041 \sqrt[3]{- \frac{465714350000000000}{17002923953354186589} + \frac{80000000 \sqrt{27417497434877861835}}{5667641317784728863}}} + \frac{805714400000}{2204082367347} + 2 \sqrt[3]{- \frac{465714350000000000}{17002923953354186589} + \frac{80000000 \sqrt{27417497434877861835}}{5667641317784728863}}}}{2}\right\} \setminus \left\{0\right\}\]

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

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