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Math Help - completing the square with an A-term co-efficient

  1. #1
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    completing the square with an A-term co-efficient

    I am trying to complete the square, just for a quadratic equation, not for a graph. i had no problem with completing the square the first time around, but suddenly, i am getting all the review questions wrong and i dont know why! here is an example:

    first, i cleared the co-efficient of the A term and came up with:

    (i took half of 2 [which is 1] and squared it [which is 1], added to both sides)




    (i rationalized and came up with):


    the book says the answer is


    where on earth did that -2 come from? all of the problems i have done have the wrong number in front of the plus/minus. i think it has something to do with the co-efficient of the A term, but i dont remember having to do anything with that. i know how to complete the square, i just dont know where that -2 came from. any insight?
    Last edited by nikki33; May 6th 2008 at 02:42 PM. Reason: looks much better now
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  2. #2
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    Quote Originally Posted by nikki33 View Post
    I am trying to complete the square, just for a quadratic equation, not for a graph. i had no problem with completing the square the first time around, but suddenly, i am getting all the review questions wrong and i dont know why! here is an example:
    2y^2+4y-3 = 0
    first, i cleared the co-efficient of the A term and came up with:
    y^2+2y = 3/2
    y^2+2y+1 = 5/2
    (i took half of 2 [which is 1] and squared it [which is 1], added to both sides)
    (y+1)^2 = 5/2
    y+1 = sqrt 5/2
    The way you are writing your answers in this form gets a bit confusing. Let me just take it from this point.
    y + 1 = \pm \sqrt{\frac{5}{2}}

    y + 1 = \pm \frac{\sqrt{10}}{2}

    y = -1 \pm \frac{\sqrt{10}}{2}

    Adding the -1 as a fraction:
    y = -\frac{2}{2} \pm \frac{\sqrt{10}}{2}

    y = \frac{-2 \pm \sqrt{10}}{2}

    -Dan
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  3. #3
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    Hello,

    y+1 = +- sqrt 5/2
    Ok !

    So y=-1 \pm \sqrt{\frac 52}=-1 \pm \sqrt{\frac{10}{4}}=-1 \pm \frac{\sqrt{10}}{2}=\frac{-{\color{red}2} \pm \sqrt{10}}{2}

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  4. #4
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    im so sorry about the confusing squares and radicals. i have changed it, a little too late, but at least now i know how to do it! my apologies.

    so, in terms of the -2 that is mystifying me, is it a -2 because the entire answer is under a 2 and if i let that -1 there, it would become -1/2? so i must change it to -2/2 (of course which is still -1) to keep the answer correct?(i hope the way im working this makes sense!) im sorry, im studying for finals and i think my head is too clogged . thank you for you time.
    Last edited by nikki33; May 6th 2008 at 02:38 PM. Reason: -
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  5. #5
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    well, i guess the reason is that my answer,


    would imply that the -1 is -1/2

    and this answer:


    implies that the -2/2 is the -1 that i originally came up with.

    if i am incorrect, please let me know. and thanks for your time.
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