Answer
$\dfrac{9}{4}$
Work Step by Step
RECALL:
To complete the square for $x^2 +mb$, just add $\left(\dfrac{m}{2}\right)^2$.
Using the rule above, the term that must be added to the given expression to complete the square is:
With $m=-3$
\begin{align*}
&=\left(\frac{-3}{2}\right)^2\\\\
&= \frac{9}{4}
\end{align*}