Answer
$\frac{9}{4}$; $(x+\frac{3}{2})^2$
Work Step by Step
To complete the square, add a term that is the square of half the coefficient of $x$ in the middle term. Then factor by trial and error.
$x^2+3x$
$(\frac{3}{2})^2=\frac{9}{4}$
$x^2+3x+\frac{9}{4}$
$(x+\frac{3}{2})^2$