Answer
$\dfrac{121}{4}$
Work Step by Step
In a perfect square trinomial $ax^2+bx+c,$ the third term is equal to $
c=\left( \dfrac{b}{2a}\right)^2.$
In the given expression, $
x^2+11x
,$ the third term, $c,$ that should be added to make the given a perfect square trinomial is
\begin{align*}
c&=\left( \dfrac{11}{2(1)}\right)^2
\\\\&=
\left( \dfrac{11}{2}\right)^2
\\\\&=
\dfrac{121}{4}
.\end{align*}
Hence, the last term that will make the given expression a perfect square trinomial is $
\dfrac{121}{4}
$.
