Answer
The constant added should be $\frac{9}{4}$
The trinomial factored is (x-$\frac{3}{2}$)$^2$
Work Step by Step
C=($\frac{b}{2}$)$^2$
C=($\frac{-3}{2}$)$^2$
C=$\frac{9}{4}$
x$^2$-3x+$\frac{9}{4}$
(x-$\frac{3}{2}$)(x-$\frac{3}{2}$)
(x-$\frac{3}{2}$)$^2$
