Question 39284
You probably meant
x^2 - 5x
The number we add is
half of -5, squared...that is
[(1/2)(-5)]^2 = (-5/2)^2 = 25/4
and is always positive.
So from x^2 - 5x + 25/4, we factor it as
(x - 5/2)^2.
Notice the -5/2 is half of the original -5 from above...