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Math Help - Solving this function with quadratic formula

  1. #1
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    Solving this function with quadratic formula

    Hi,

    I have been sitting at this function for a couple of hours, trying to solve it.

    0.1w^2 + 2155w + 20

    I am kind of dumbfounded by this. Even if I factor out the 0.1, I cannot figure this out.

    Appreciate your help,

    Alex
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  2. #2
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    Quote Originally Posted by alex95 View Post
    Hi,

    I have been sitting at this function for a couple of hours, trying to solve it.

    0.1w^2 + 2155w + 20

    I am kind of dumbfounded by this. Even if I factor out the 0.1, I cannot figure this out.

    Appreciate your help,

    Alex
    \displaystyle x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}

    Did you just plug int he numbers?
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  3. #3
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    Quote Originally Posted by alex95 View Post
    Hi,

    I have been sitting at this function for a couple of hours, trying to solve it.

    0.1w^2 + 2155w + 20

    I am kind of dumbfounded by this. Even if I factor out the 0.1, I cannot figure this out.

    Appreciate your help,

    Alex

    0.1\left(w^2+21550w\right)+20=0.1\left(w^2+10775w+  10775w\right)+20

    =0.1\left(w^2+21550w+10775^2-10775^2\right)+20

    =0.1\left(w+10775\right)^2-(0.1)10775^2+20

    Are you trying to factor, or is the expression equal to something ?
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  4. #4
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    Yes, equal to 200

    Thanks,

    Alex
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  5. #5
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    Now it's equal to something you can put into the form ax^2+bx+c = 0 by subtracting 200 from both sides

    0.1w^2 + 2155w + 20 = 200 becomes 0.1w^2+2155w-180 = 0 then plug and chug.

    Of course 2155^2 >> 4 \cdot 0.1 \cdot -180 which means \pm \sqrt{b^2-4ac} \approx \pm b
    Last edited by e^(i*pi); January 24th 2011 at 02:44 PM. Reason: put 200, not 180
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  6. #6
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    Ok,

    well you can set it up using dwsmith's method, which applies the "abc robot"
    but the expression must be equal to zero to use that.

    0.1w^2+2155w+20=200\Rightarrow\ 0.1w^2+2155w+20-200=200-200=0

    Multiplying zero by anything is zero, so multiply by 10 for convenience

    w^2+21550w-1800=0

    aw^2+bw+c=0

    a=1,\;\;\;b=21550,\;\;\;c=-1800


    Alternatively,

    0.1(w+10775)^2=200-20+(0.1)10775^2

    Multiply both sides by 10.
    Take square roots and finally subtract 10775 from both sides.
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