1. ## rational equation

I know it's probably that time of the night where I should just sit back and leave it alone and it would come to me in the morning but I am obsessing over this. I keep getting stuck in this equation. Can someone help me out. I just can't seem to isolate this variable.

$\displaystyle 22x-\frac {8640}{x^2} -\frac {6220800}{x^4} = 0$

$\displaystyle 22x = \frac {8640}{x^2} + \frac {6220800}{x^4}$

$\displaystyle 22x^5 = \frac {8640x^4}{x^2} + 6220800$

$\displaystyle 22x^5 = 8640x^2 + 6220800$

$\displaystyle 22x^5-8640x^2 = 6220800$ ...And this is where I am getting stuck.

Sincerely,

Raymond

2. ## Re: rational equation

Originally Posted by raymac62
I know it's probably that time of the night where I should just sit back and leave it alone and it would come to me in the morning but I am obsessing over this. I keep getting stuck in this equation. Can someone help me out. I just can't seem to isolate this variable.

$\displaystyle 22x-\frac {8640}{x^2} -\frac {6220800}{x^4} = 0$

$\displaystyle 22x = \frac {8640}{x^2} + \frac {6220800}{x^4}$

$\displaystyle 22x^5 = \frac {8640x^4}{x^2} + 6220800$

$\displaystyle 22x^5 = 8640x^2 + 6220800$

$\displaystyle 22x^5-8640x^2 = 6220800$ ...And this is where I am getting stuck.
... and you will get "stucK'.

this is a fifth degree polynomial equation. there is no easy solution "by hand".

$\displaystyle 22x^5 - 8640x^2 - 6220800 = 0$

$\displaystyle 11x^5 - 4320x^2 - 3110400 = 0$

use a calculator to solve this, $\displaystyle x \approx 12.828143$