# How do I solve quadratics by completing the squares? I’ve looked it up, but I don’t get it and I have homework due on it?

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### Dr. Badi M

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Best to give an example x^2 -6x +8=0 can factorise it easily but by completing the square you do this (x-3)^2 +8 -9 =0 so (x-3)^2 - 1= 0 So basically you half the number of the middle term with x you put in a bracket so when you square it you get the +9 so you need to subtract this then you shift to RHS and solve: (x-3)^2 - 1 = 0 Therefore (x-3)^2 = 1 So (x-3) = + or - Sqr(1) Gives x = 3 + or - 1 x = 3 + 1= 4 Or x = 3 - 1 = 2 of course in this case much easier to factorise and get solution as a check x^2 -6x +8=0 this factorises to (x-4)(x- 2)=0 Giving x= 4 or x=2

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