250 = 3.077*0.25*(x-20)+0.70*5.677*10^-8*0.25(x^4-283^4)

asked by guest
on Oct 21, 2024 at 11:44 am



You asked:

Solve the equation \(250 = 3.077 \cdot 0.25 \cdot \left(x - 20\right) + 0.70 \cdot 5.677 \cdot {10}^{-8} \cdot 0.25 \cdot \left({x}^{4} - {283}^{4}\right)\) for the variable \(x\).

MathBot Answer:

The 4 solutions to the equation are: \[\begin{aligned}x &= \frac{\sqrt{- 2 \sqrt[3]{\frac{591745562500000000000000}{1579188121} + \frac{\sqrt{3707942679645074754423292102511319510560892330963}}{1579188121}} + \frac{6154000000000}{39739 \sqrt{2 \sqrt[3]{\frac{591745562500000000000000}{1579188121} + \frac{\sqrt{3707942679645074754423292102511319510560892330963}}{1579188121}} - \frac{877623865421746}{39739 \sqrt[3]{\frac{591745562500000000000000}{1579188121} + \frac{\sqrt{3707942679645074754423292102511319510560892330963}}{1579188121}}}}} + \frac{877623865421746}{39739 \sqrt[3]{\frac{591745562500000000000000}{1579188121} + \frac{\sqrt{3707942679645074754423292102511319510560892330963}}{1579188121}}}}}{2} - \frac{\sqrt{2 \sqrt[3]{\frac{591745562500000000000000}{1579188121} + \frac{\sqrt{3707942679645074754423292102511319510560892330963}}{1579188121}} - \frac{877623865421746}{39739 \sqrt[3]{\frac{591745562500000000000000}{1579188121} + \frac{\sqrt{3707942679645074754423292102511319510560892330963}}{1579188121}}}}}{2} \approx 309.43173\\x &= - \frac{\sqrt{2 \sqrt[3]{\frac{591745562500000000000000}{1579188121} + \frac{\sqrt{3707942679645074754423292102511319510560892330963}}{1579188121}} - \frac{877623865421746}{39739 \sqrt[3]{\frac{591745562500000000000000}{1579188121} + \frac{\sqrt{3707942679645074754423292102511319510560892330963}}{1579188121}}}}}{2} - \frac{\sqrt{- 2 \sqrt[3]{\frac{591745562500000000000000}{1579188121} + \frac{\sqrt{3707942679645074754423292102511319510560892330963}}{1579188121}} + \frac{6154000000000}{39739 \sqrt{2 \sqrt[3]{\frac{591745562500000000000000}{1579188121} + \frac{\sqrt{3707942679645074754423292102511319510560892330963}}{1579188121}} - \frac{877623865421746}{39739 \sqrt[3]{\frac{591745562500000000000000}{1579188121} + \frac{\sqrt{3707942679645074754423292102511319510560892330963}}{1579188121}}}}} + \frac{877623865421746}{39739 \sqrt[3]{\frac{591745562500000000000000}{1579188121} + \frac{\sqrt{3707942679645074754423292102511319510560892330963}}{1579188121}}}}}{2} \approx -520.56513\\x &= \frac{\sqrt{- \frac{877623865421746}{39739 \sqrt[3]{\frac{591745562500000000000000}{1579188121} + \frac{\sqrt{3707942679645074754423292102511319510560892330963}}{1579188121}}} + 2 \sqrt[3]{\frac{591745562500000000000000}{1579188121} + \frac{\sqrt{3707942679645074754423292102511319510560892330963}}{1579188121}}}}{2} - \frac{i \sqrt{- \frac{877623865421746}{39739 \sqrt[3]{\frac{591745562500000000000000}{1579188121} + \frac{\sqrt{3707942679645074754423292102511319510560892330963}}{1579188121}}} + 2 \sqrt[3]{\frac{591745562500000000000000}{1579188121} + \frac{\sqrt{3707942679645074754423292102511319510560892330963}}{1579188121}} + \frac{6154000000000}{39739 \sqrt{- \frac{877623865421746}{39739 \sqrt[3]{\frac{591745562500000000000000}{1579188121} + \frac{\sqrt{3707942679645074754423292102511319510560892330963}}{1579188121}}} + 2 \sqrt[3]{\frac{591745562500000000000000}{1579188121} + \frac{\sqrt{3707942679645074754423292102511319510560892330963}}{1579188121}}}}}}{2} \approx 105.5667 -441.03555 i\\x &= \frac{\sqrt{- \frac{877623865421746}{39739 \sqrt[3]{\frac{591745562500000000000000}{1579188121} + \frac{\sqrt{3707942679645074754423292102511319510560892330963}}{1579188121}}} + 2 \sqrt[3]{\frac{591745562500000000000000}{1579188121} + \frac{\sqrt{3707942679645074754423292102511319510560892330963}}{1579188121}}}}{2} + \frac{i \sqrt{- \frac{877623865421746}{39739 \sqrt[3]{\frac{591745562500000000000000}{1579188121} + \frac{\sqrt{3707942679645074754423292102511319510560892330963}}{1579188121}}} + 2 \sqrt[3]{\frac{591745562500000000000000}{1579188121} + \frac{\sqrt{3707942679645074754423292102511319510560892330963}}{1579188121}} + \frac{6154000000000}{39739 \sqrt{- \frac{877623865421746}{39739 \sqrt[3]{\frac{591745562500000000000000}{1579188121} + \frac{\sqrt{3707942679645074754423292102511319510560892330963}}{1579188121}}} + 2 \sqrt[3]{\frac{591745562500000000000000}{1579188121} + \frac{\sqrt{3707942679645074754423292102511319510560892330963}}{1579188121}}}}}}{2} \approx 105.5667 + 441.03555 i\end{aligned}\]

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

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