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Math Help - Simple Quadratic Equation(s)

  1. #1
    Raj
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    Simple Quadratic Equation(s)

    Determine the roots of the equations, use any method (complete sq, factor, quad. formula) :

    A) 50x^2-2x-77=0

    I came up with the below using the quadratic formula. Just need to know how to get it to its simplest form.

    (2+{\sqrt{15404}})/(100)

    B)  (x-1/x+4) - (x/x-3) = 9

    (x-1)(x-3)-(x)(x+4) = 9(x+4)(x-3)
    (x^2-4x+3)-(x^2+4x) = 9(x^2+x-12)
    (x^2-4x+3)-(x^2+4x) = (9x^2+9x-108)
    New Equation: 9x^2+9x-111 = 0 ?

    If somone could check if i did the algebra right for the new equation i would be thankfull.
    Last edited by Raj; October 12th 2007 at 09:25 AM.
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  2. #2
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    Quote Originally Posted by Raj View Post
    Determine the roots of the equations, use any method (complete sq, factor, quad. formula) :

    A) 50x^2-2x-77=0

    I came up with the below using the quadratic formula. Just need to know how to get it to its simplest form.

    (2+{\sqrt{15404}})/(100)

    B)  (x-1/x+4) - (x/x-3) = 9

    (x-1)(x-3)-(x)(x+4) = 9(x+4)(x-3)
    (x^2-4x+3)-(x^2+4x) = 9(x^2+x-12)
    (x^2-4x+3)-(x^2+4x) = (9x^2+9x-108)
    New Equation: 9x^2+9x-111 = 0 ?

    If somone could check if i did the algebra right for the new equation i would be thankfull.
    Hello,

    A) there is missing the solution x = (2-{\sqrt{15404}})/(100)

    B) You did all the calculations really fine except the last line:

    (x^2-4x+3)-(x^2+4x) = (9x^2+9x-108)~\iff~-8x+3 = 9x^2+9x-108 . that means you have to solve for x:

    9x^2+17x-111 = 0 . I leave this for you
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  3. #3
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Raj View Post
    (2+{\sqrt{15404}})/(100)
    As earboth said you are missing the other solution.

    The question remains though, if this is in its simplest form.

    \frac{2 \pm \sqrt{15404}}{100} = \frac{2 \pm \sqrt{4 \cdot 3851}}{100}

    = \frac{2 \pm 2 \sqrt{3851}}{100} = \frac{1 \pm \sqrt{3851}}{50}

    By the way. A quick way to note that 15404 is divisible by 4 is to look at the last two digits. If this number is divisible by 4 then the whole number is divisible by 4.

    -Dan
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  4. #4
    Raj
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    @Earboth

    Thankyou, i wasn't sure if i needed to distribute the (-) to the +4x.

    @Topsquark

    Yea i still dont know all of the math tags so i left out the \pm. Thanks for confirming the answer, and the tip
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