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Thread: solving quadratic functions through the use of factoring

  1. #1
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    solving quadratic functions through the use of factoring

    Hello,

    I was practicing how to solve quadratic equations as part of some summer review, but then I stumbled across this equation...

    1/2x(x+30)=2,700

    I am supposed to solve the equation above using factoring, but I'm not quite sure how to do this. I tried solving it myself by first multiplying by 2 to eliminate the 1/2, and I eventually get x=-60 and x=90 as my answers, but I don't think those are correct.

    Any clues?
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  2. #2
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    Re: solving quadratic functions through the use of factoring

    Multiply out by 2:

    $x(x+30) = 5400$

    Distribute the $x$:

    $x^2+30x = 5400$

    Subtract 5400 from both sides:

    $x^2+30x-5400=0$

    90 and 60 are factors of 5400 that are 30 apart:

    $(x+90)(x-60) = 0$

    Your answers were close, but you got the signs wrong. It should be $x=-90,x=60$
    Thanks from oneonethree
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  3. #3
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    Re: solving quadratic functions through the use of factoring

    Yes, the first step is to multiply by 2 (I assume you mean (1/2)x(x+ 30) rather than 1/(2x(x+30)) so this x(x+ 30)= 5400.
    But the basic rule for solving equations by "factoring" is that "if ab= 0 then a= 0 or b= 0". So the first thing you need to do is "unfactor" so that you can subtract 5400 from each side. x(x+ 30)= x^2+ 30x= 5400. Then x^2+ 30x- 5400= 0. That is what you want to factor. (It helps to know that 90*60= 5400.)
    Thanks from oneonethree
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