decide what number must be added to the binomial to make a perfect square x^2+(3/2)x
The general form of a 2nd degree polynomial that is a perfect square is Ax2 + 2ACx + C2.
In this case, 2AC = 3/2. Since A = 1,
2C = 3/2 and C = 3/4
So the number that needs to be added is C2 = (3/4)2 = 9/16
and our polynomial is x2+ (3/2)x + 9/16