Lösung 2.3:1c

Aus Online Mathematik Brückenkurs 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−12−1 

This means that

5+2x−x2=5−x2−2x=5−x−12−1=5−x−12+1=6−x−12

A quick check shows that we have completed the square correctly.:

6−x−12=6−x2−2x+1=6−x2+2x−1=5+2x−x2