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How would one factor this by hand

  1. Feb 29, 2008 #1
    [SOLVED] How would one factor this.. by hand..

    Assuming I didn't know the perfect square formula ( (a+-b)^2), how would I go about solving this equation by hand factoring?

    x^2 + b/a *x + b^2 / 4a^2 = 0

    I am trying to figure out how the quadratic formula is derived, and this is one part of deriving the equation in which I am unable to hand factor(assuming I didn't know perfect squares formula), how would one go about doing this ?

    It is included on a website(step 3 and 4), http://www.1728.com/quadr2.gif

    Can someone show me the steps to factoring that by hand?
  2. jcsd
  3. Feb 29, 2008 #2
    how about (x+b/(2a))^2
  4. Feb 29, 2008 #3

    Gib Z

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    Homework Helper

    Do you what "completing the square" is?

    Wait, are you asking for a method to do with without assuming you know [tex](a+b)^2 = a^2 + 2ab + b^2[/tex]? If you don't want to assume it, just show it first. Expand.

    [tex](a+b)^2 = (a+b)(a+b) = a(a+b) + b(a+b) = a^2 + ab + ab + b^2 = a^2 + 2ab + b^2[/tex].
    Last edited: Feb 29, 2008
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