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Math Help - Solving for a variable with quadratic equations

  1. #1
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    Solving for a variable with quadratic equations

    Solving for t

    A = 6.5 - \frac{20.4t}{t^2+36}

    I wasn't sure but I decided to try to get the fraction out by multiplying both sides by t^2+36

    Which makes it:

    A(t^2+36) = 6.5(t^2+36) - 20.4t

    I then distributed accordingly.

    At^2 + A36 = 6.5t^2 + 234 - 20.4t

    I don't know if I'm doing this correctly or where to go next. Help appreciated immensely. <3
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  2. #2
    Senior Member Educated's Avatar
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    You are on the right track.

    Move everything to one side and factorise to get the formula to look similar to: (a)t^2 + (b)t + (c) = 0
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  3. #3
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    Move everything to one side.

    \displaystyle At^2 + A36 = 6.5t^2 + 234 - 20.4t

    \displaystyle At^2 + A36 - 6.5t^2 - 234 + 20.4t= 0

    now group in order of t

    \displaystyle At^2  - 6.5t^2  + 20.4t+ A36- 234= 0

    Factoring

    \displaystyle (A  - 6.5)t^2  + 20.4t+ A36- 234= 0

    Now in the quadratic formula make \displaystyle a = A  - 6.5 , b  =20.4, c= A36- 234= 0
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  4. #4
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    Thanks guys.

    I get to here:
    \frac{-20.4  \sqrt{20.4^2 - 4 (A-6.5)(A36-234)}}{2 (A-6.5)}

    Do I foil and multiply out? This problem frustrates me.
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  5. #5
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    Not unless you have so good reason to do so. That is the answer.
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