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Math Help - Completing the square

  1. #1
    AliceD
    Guest

    Red face Completing the square

    Hi, this a basic question but Im just not getting it for some reason and it's keeping me from moving forward with the mountain of math HW I have. Its an example problem
    f (x) = 2x^2 + 8x+5 then it is factored out
    f (x) =2(x^2+4x) +5 the the square is completed to form
    f (x) = 2(x^2+4x+4) +5-8 and I dont understand where the 8 comes from
    the it is reduced down to
    2(x+2)^2-3 and I get how 5-8 equals -3 but how is the rest of it reduced down to that? What happened to the 4x?

    Any insight is very much appreciated!! Hope everyone is having a nice sunday morning!
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  2. #2
    Newbie
    Joined
    Jan 2013
    From
    United States
    Posts
    10

    Re: Completing the square

    The 8 comes from 4*2, which is in the parentheses. 2(x^2+4x+4)
    In the final step, you can square x+2 using FOIL (First, Outer, Inner, Last). So, x*x+x*2+x*2+2*2=x^2+4x+4, which would be what is multiplied by 2 in the step before.
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