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Math Help - rational equation

  1. #1
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    Thumbs up 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.

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

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

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

      22x^5 = 8640x^2 + 6220800

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

    Thanks in advance,

    Sincerely,

    Raymond
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  2. #2
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    Re: rational equation

    Quote Originally Posted by raymac62 View Post
    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.

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

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

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

      22x^5 = 8640x^2 + 6220800

    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".

    22x^5 - 8640x^2 - 6220800 = 0

    11x^5 - 4320x^2 - 3110400 = 0

    use a calculator to solve this, x \approx 12.828143
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