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Math Help - reducing quadratic

  1. #1
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    reducing quadratic

    hello, I have this quadratic:
    -180x^2 + 12000x - 100000

    What is the best way of reducing this down as much as possible so I more easily solve it ?

    I see I could factor out 20 eg. 20(-90x^2 + 600x - 5000), but is there a more effective way of reducing it ?

    thanks for any help.
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  2. #2
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    Re: reducing quadratic

    Why not take out another factor of 10?
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  3. #3
    Member sbhatnagar's Avatar
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    Re: reducing quadratic

    -180x^2+12000x-100000

    Take out a factor of -180

    = -180\left (x^2-\frac{12000}{180}x+\frac{100000}{180} \right)

    = -180\left (x^2-\frac{200}{3}x+\frac{5000}{9} \right)

    = -180\left (x^2-\frac{200}{3}x+\frac{5000}{9} +\frac{40000}{36}-\frac{40000}{36}\right)

    = -180\left( \frac{36x^2-24000x+40000}{36}-\frac{20000}{36}\right)

    = -180\left[ \left(\frac{6x-200}{6}\right)^2-\left(\frac{100\sqrt{2}}{6}\right)^2 \right]

    Now, use difference of squares to factorize the expression.
    Last edited by sbhatnagar; December 11th 2011 at 12:01 AM. Reason: leaving something for the OP to do...
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