# Problem of the Week

## Updated at Nov 5, 2018 11:02 AM

How would you solve $$\frac{20}{x}-2-{x}^{2}=4$$?

Below is the solution.

$\frac{20}{x}-2-{x}^{2}=4$

1
Multiply both sides by $$x$$.
$20-2x-{x}^{3}=4x$

2
Move all terms to one side.
$20-2x-{x}^{3}-4x=0$

3
Simplify  $$20-2x-{x}^{3}-4x$$  to  $$20-6x-{x}^{3}$$.
$20-6x-{x}^{3}=0$

4
Factor $$20-6x-{x}^{3}$$ using Polynomial Division.
$(-{x}^{2}-2x-10)(x-2)=0$

5
Solve for $$x$$.
$x=2$

6
Use the Quadratic Formula.
$x=\frac{2+6\imath }{-2},\frac{2-6\imath }{-2}$

7
Collect all solutions from the previous steps.
$x=2,\frac{2+6\imath }{-2},\frac{2-6\imath }{-2}$

8
Simplify solutions.
$x=2,-1-3\imath ,-1+3\imath$

Done