Problem of the Week

Updated at Jul 8, 2019 5:12 PM

How can we solve the equation \(4{u}^{2}-\frac{20}{u}=59\)?

Below is the solution.



\[4{u}^{2}-\frac{20}{u}=59\]

1
Multiply both sides by \(u\).
\[4{u}^{3}-20=59u\]

2
Move all terms to one side.
\[4{u}^{3}-20-59u=0\]

3
How?
Factor \(4{u}^{3}-20-59u\) using Polynomial Division.
\[(4{u}^{2}+16u+5)(u-4)=0\]

4
Solve for \(u\).
\[u=4\]

5
How?
Use the Quadratic Formula.
\[u=\frac{-16+4\sqrt{11}}{8},\frac{-16-4\sqrt{11}}{8}\]

6
Collect all solutions from the previous steps.
\[u=4,\frac{-16+4\sqrt{11}}{8},\frac{-16-4\sqrt{11}}{8}\]

7
Simplify solutions.
\[u=4,-\frac{4-\sqrt{11}}{2},-\frac{4+\sqrt{11}}{2}\]

Done

Decimal Form: 4, -0.341688, -3.658312