Aus Online Mathematik Brückenkurs 1

By completing the square, the second degree polynomial can be rewritten as a quadratic plus a constant, and then it is relatively straightforward to read off the expression's minimum value,

\displaystyle x^{2}-4x+2 = (x-2)^{2}-2^{2}+2 = (x-2)^{2}-2\,\textrm{.}

Because \displaystyle (x-2)^{2} is a quadratic, this term is always larger than or equal to 0 and the whole expression is therefore at least equal to -2, which occurs when \displaystyle x-2=0 and the quadratic is zero, i.e. \displaystyle x=2.