Processing Math: Done

From Förberedande kurs i matematik 1

When we complete the square, it is only the first two terms, x2+2x , that are involved. The general formula for completing the square states that x2+ax equals

x+2a2−2a2 

Note how the coefficient a in front of the x turns up halved in two places.

If we use this formula, we obtain

x2+2x=x+222−222=x+12−1 

and if we subtract the last " 1 " , we obtain

x2+2x−1=x+12−1−1=x+12−2 

To be completely certain that we have used the correct formula, we can expand the quadratic on the right-hand side,

x+12−2=x2+2x+1−2=x2+2x−1 

and see that the relation really holds.