How would one factor this by hand

[razored]

[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?

 

[stakehoagy]

how about (x+b/(2a))^2

 

[Gib Z]

Do you what "completing the square" is?

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

$$(a+b)^2 = (a+b)(a+b) = a(a+b) + b(a+b) = a^2 + ab + ab + b^2 = a^2 + 2ab + b^2$$.