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Math Help - Help with daughter's homework

  1. #1
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    Help with daughter's homework

    I was trying to help my daughter solve a problem from her algebra homework. The answer I found through trial and error as well as from another site (c = 40.5511), but the steps to get there have confounded me.

    0.01 = -0.027c^2 + 8c - 280

    Any guidance or suggestions would be appreciated.
    Last edited by Embalmed; February 5th 2008 at 08:49 PM.
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  2. #2
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    Try wrapping [ math] and [/ math] tags around the problem, it's easier to read :P

    (remove spaces in tags)
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  3. #3
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Embalmed View Post
    I was trying to help my daughter solve a problem from her algebra homework. The answer I found through trial and error as well as from another site (c = 40.5511), but the steps to get there have confounded me.

    0.01 = -0.027c^2 + 8c - 280

    Any guidance or suggestions would be appreciated.
    first subtract 0.01 from both sides to get -0.027c^2 + 8c - 280.01 = 0

    now use the quadratic formula

    the quadratic formula says, the solutions to a quadratic equation of the form ax^2 + bx + c = 0 are given by:

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

    can you continue?
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  4. #4
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    Quote Originally Posted by Embalmed View Post
    I was trying to help my daughter solve a problem from her algebra homework. The answer I found through trial and error as well as from another site (c = 40.5511), but the steps to get there have confounded me.

    0.01 = -0.027c^2 + 8c - 280

    Any guidance or suggestions would be appreciated.
    Hi,

    this is a quadratic equation (and honestly one of the ugliest I've seen at this forum )

    There exist a formula to solve quadratic equations:

    If the equation is in the form

    ax^2 + bx + c = 0 then the solutions are:

    x_1=\frac{-b + \sqrt{b^2-4ac}}{2a}~\vee~ x_2=\frac{-b - \sqrt{b^2-4ac}}{2a}

    To your question:

    1. Bring your equation into the required form:

    0.01 = -0.027c^2 + 8c - 280~\iff~  -0.027c^2 + 8c - 280.01 = 0

    2. Now plug in the values into the formula:

    x_1=\frac{-8 + \sqrt{8^2-4\cdot (-0.027) \cdot 280.01}}{2 \cdot (-0.027)}~\vee~ x_2=\frac{-8 - \sqrt{8^2-4\cdot (-0.027) \cdot 280.01}}{2 \cdot (-0.027)}

    3. Use a calculator. You'll get:

    x_1 \approx 40.55106148...~\vee~ x_2 \approx 255.7452348...
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  5. #5
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    Thanks!

    OMG, that was so many years ago. It is no wonder I forgot. When I read the formula I could hear it in my head from my teacher so long ago. Thanks so much!
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  6. #6
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    Hello, Embalmed!

    I was trying to help my daughter solve a problem from her algebra homework.

    0.01 \:= \:-0.027c^2 + 8c - 280

    Answer: . c \,= \,40.5511

    I would immediately multiply by 1000 ... and get: . 10 \:=\:-27c^2 + 8,000c - 280,000

    Then we have the quadratic: . 27c^2 - 8000c + 280,000 \:=\:0

    Quadratic Formula: . c \;=\;\frac{8000 \pm\sqrt{8000^2 - 4(27)(280,000)}}{2(27)} \;=\;\frac{8000 \pm\sqrt{33,758,920}}{54}

    And there are two solutions: . \begin{Bmatrix}255.7452348 \\ \text{and} \\ 40.55106148\end{Bmatrix}

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