Processing Math: Done

From Förberedande kurs i matematik 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,

x2−4x+2=(x−2)2−22+2=(x−2)2−2.

Because (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 x−2=0 and the quadratic is zero, i.e. x=2.