completing the square... :) Watch

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Kirjava
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#1
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Hey

I'm at GCSE, and I was doing some quadratic equations and thought... 'where does this formula come from?!'

This, being a question that I don't need to know the answer to, is obviously something I tried to find out straight away See the attachment ( this is a screengrab from a PDF located at http://www.mis.coventry.ac.uk/jtm/1/lec1p6.pdf ) for what I found.

I don't understand how you get from the first step to the second step (or the fifth to the sixth, but that doesn't matter right now). I understand it's a process called completing the square, but I really can't see how it works without perfect squares... Any help would be greatly appreciated.
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DaveManUK
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completing the square; rewriting a quadratic of the form ax^2+bx+c=0 in the form

a(x^2+b/a+c/a)=0 so the x^2 coefficient is 1.
a[(x+b/2a)^2-excess terms+c/a]=0 - that is completing the square. half of the x term goes inside the brackets.

eg. x^2+6x+5=0
(x+3)^2 -9 + 5=0 - see, hald the x term inside, and take off excess term u get when you expand the bracket.s
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ljfrugn
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Yeah, it comes in handy for finding the min (or max) values of a quadratic (or i suppose quartic or other even-ordered powers) function.
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