Question 30611
To make{{{x^2+3x}}} into a perfect square trinomial, you need to add the square of half the coefficient of x.  The coefficient of x is 3, so the square of half that is {{{(3/2)^2 = 9/4}}}

Check:
{{{x^2 + 3x + 9/4 = (x + 3/2)(x + 3/2)}}} = {{{(x + 3/2)^2}}}