How would one factor this by hand

  • Thread starter razored
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  • #1
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[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" [Broken]

Can someone show me the steps to factoring that by hand?
 
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Answers and Replies

  • #2
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how about (x+b/(2a))^2
 
  • #3
Gib Z
Homework Helper
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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].
 
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