nLab completing the square

Given a field KK whose characteristic is not 2, let pK[x]p\in K[x] be a polynomial over KK with value p=12ax 2bxp = \tfrac{1}{2} a x^2 - b x. Then

12ax 2bx=12a(xba) 2b 22a \tfrac{1}{2} a x^2 - b x = \tfrac{1}{2} a(x - \tfrac{b}{a})^2 - \tfrac{b^2}{2a}


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