Answer
$25$
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^2-10x
,$ the third term, $c,$ that should be added to make the given a perfect square trinomial is
\begin{align*}
c&=\left( \dfrac{-10}{2(1)}\right)^2
\\\\&=
\left( \dfrac{-10}{2}\right)^2
\\\\&=
\left( -5\right)^2
\\\\&=
25
.\end{align*}
Hence, the last term that will make the given expression a perfect square trinomial is $
25
$.