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Math Help - solving equations

  1. #1
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    solving equations

    I have worked on my math for 8 hours straight.. my brain has melted but I learned a lot today. I have 2 problems left and can not seem to get them... Can anyone show me how to work them out?

    1) solve the quadratic equation...

    4xsquared=13x +12


    and the other is...
    2) Factor Completly

    9x squared+12xy+4y squared-25

    I dont have long to turn this in so it is kind of urgent.. any help is GREATLY appreciated.. Thanks so much.. Heather
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  2. #2
    MHF Contributor red_dog's Avatar
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    1) 4x^2=13x+12\Leftrightarrow 4x^2-13x-12=0
    a=4, \ b=-13, \ c=-12
    \Delta=b^2-4ac=361=19^2
    x_{1,2}=\frac{-b\pm\sqrt{\Delta}}{2a}
    Find x_1, \ x_2

    2) 9x^2+12xy+4y^2-25=(3x+2y)^2-5^2
    Now, use the identity a^2-b^2=(a-b)(a+b)
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  3. #3
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    I dont have a clue what the first problem means or what the answer is.. it looks very confusing..
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  4. #4
    MHF Contributor red_dog's Avatar
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    If you don't know the formulas for the quadratic equation, let's try to factorise the equation:
    4x^2-13x-12=0\Leftrightarrow 4x^2-16x+3x-12=0\Leftrightarrow
    \Leftrightarrow 4x(x-4)+3(x-4)=0\Leftrightarrow (x-4)(4x+3)=0
    Now, x-4=0\Rightarrow x=4

    or 4x+3=0\Rightarrow x=-\frac{3}{4}


    Edited
    (Thanks, flyingsquirrel)
    Last edited by red_dog; July 2nd 2008 at 11:13 PM.
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  5. #5
    Super Member flyingsquirrel's Avatar
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    Just a little typo :
    Quote Originally Posted by red_dog View Post
    {\color{red}4}x^2-13x-12=0\Leftrightarrow {\color{red}4}x^2-16x+3x-12=0
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