# How do you complete the square?

Completing the square is taking an equation in the form a1x2+b1x+c1 and butting it into the form a2(x+b2)2+c2Let's try an example:x2+4x+5First step is to make sure the coefficient of x2 is 1. In this case it's already done.Secondly we half the coefficient of x, and put that number into our brackets:(x+2)2+const.= x2+4x+5Now if we expand the left hand side of the equation, we can work out what constant to put at the end(x+2)2= x2+4x+4, but we want x2+4x+5. To make this we add 1 as our constant.Final answer: x2+4x+5=(x+2)2+1(I would then go on to have them work through a couple of examples to check their basic understanding, before moving onto examples where coefficient of x2 is larger than 1, and where coefficient of x is odd or negative. In each case I would allow them to work it through themselves as much as possible and only prompt where necessary, since practice is the best way to solidify an idea.)

Answered by Annabelle B. Maths tutor

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