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Math Help - tricky algebraic manipulation

  1. #1
    jut
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    tricky algebraic manipulation

    I need this \frac{-18477 s-2.82843\times 10^8}{s^2+15307 s+4.\times 10^8} to be in this format : \frac{s+a}{(s+a)^2+w^2}

    I can easily factor the top to get the "s+a",

    -18477\frac{s+15307 }{s^2+15307s+4*10^8}

    Now (s+15307)^2=s^2+30614 s+234304249

    but how can I factor the bottom in such a way to get the required form? Can someone help please?
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  2. #2
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    Have you tried completing the square? Do the numbers have to be integers?

     s^2+15307s+4\times10^8 = (s^2 + 15307s + 7653.5^2) - 7653.5 ^2 + 4 \times 10^8

     (s+ 7653.5)^2 + (4 \times 10^8 - 7653.5^2)
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  3. #3
    jut
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    Quote Originally Posted by Gusbob View Post
    Have you tried completing the square? Do the numbers have to be integers?

     s^2+15307s+4\times10^8 = (s^2 + 15307s + 7653.5^2) - 7653.5 ^2 + 4 \times 10^8

     (s+ 7653.5)^2 + (4 \times 10^8 - 7653.5^2)

    Good idea.

    So I get:

    -18477\frac{s+15307 }{(s+7653)^2+18477^2}

    which is tantalizingly close, but not in the required form.
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  4. #4
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    Sorry I didn't read the question carefully. Didn't realise the square on the bottom has to be the square of the numerator.

    In this case, I don't think it will be possible to make it into the format you wish, unless 'w' can have 's' in it.

    This is because we cannot make the bottom square  (s + 15307)^2 without introducing more 's' into the denominator, which would have to be part of 'w'.
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  5. #5
    jut
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    It's ok, thanks for the help anyway.

    Yeah I was beginning to think it's not possible too. Oh well.
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