Processing Math: Done

From Förberedande kurs i matematik 1

As always when completing the square, we focus on the quadratic and linear terms 2x−x2, which we also can write as −(x2−2x). If we neglect the minus sign, we can complete square of the expression 2x−x2 by using the formula

x2−ax=x−2a2−2a2

and we obtain

x2−2x=x−222−222=(x−1)2−1.

This means that

5+2x−x2=5−(x2−2x)=5−(x−1)2−1=5−(x−1)2+1=6−(x−1)2.

A quick check shows that we have completed the square correctly

6−(x−1)2=6−(x2−2x+1)=6−x2+2x−1=5+2x−x2.