55.6*10^3=0.2729*v^2+(11.6*10^7/v^2)
You asked:
Solve the equation \(55.6 \cdot {10}^{3} = 0.2729 \cdot {v}^{2} + \frac{11.6 \cdot {10}^{7}}{{v}^{2}}\) for the variable \(v\).
MathBot Answer:
The 4 solutions to the equation are: \[\begin{aligned}v &= - 200 \sqrt{\frac{6950}{2729} - \frac{5 \sqrt{1852959}}{2729}} \approx -45.914536\\v &= 200 \sqrt{\frac{6950}{2729} - \frac{5 \sqrt{1852959}}{2729}} \approx 45.914536\\v &= - 200 \sqrt{\frac{6950}{2729} + \frac{5 \sqrt{1852959}}{2729}} \approx -449.03172\\v &= 200 \sqrt{\frac{6950}{2729} + \frac{5 \sqrt{1852959}}{2729}} \approx 449.03172\end{aligned}\]