Problem of the Week

Updated at Nov 5, 2018 11:02 AM

How would you solve 20x2x2=4\frac{20}{x}-2-{x}^{2}=4?

Below is the solution.



20x2x2=4\frac{20}{x}-2-{x}^{2}=4

1
Multiply both sides by xx.
202xx3=4x20-2x-{x}^{3}=4x

2
Move all terms to one side.
202xx34x=020-2x-{x}^{3}-4x=0

3
Simplify  202xx34x20-2x-{x}^{3}-4x  to  206xx320-6x-{x}^{3}.
206xx3=020-6x-{x}^{3}=0

4
Factor 206xx320-6x-{x}^{3} using Polynomial Division.
(x22x10)(x2)=0(-{x}^{2}-2x-10)(x-2)=0

5
Solve for xx.
x=2x=2

6
Use the Quadratic Formula.
x=2+6ı2,26ı2x=\frac{2+6\imath }{-2},\frac{2-6\imath }{-2}

7
Collect all solutions from the previous steps.
x=2,2+6ı2,26ı2x=2,\frac{2+6\imath }{-2},\frac{2-6\imath }{-2}

8
Simplify solutions.
x=2,13ı,1+3ıx=2,-1-3\imath ,-1+3\imath

Done