Answer
$x^2-\dfrac{4}{5}x+\dfrac{4}{25}
\Rightarrow\left(
x-\dfrac{2}{5} \right)^2
$
Work Step by Step
The third term of a perfect square trinomial is equal to the square of half the coefficient of the middle term. Hence, to complete the square of the given expression $
x^2-\dfrac{4}{5}x
,$ the third term must be
\begin{array}{l}\require{cancel}\left(
\dfrac{-4/5}{2}\right)^2
\\\\=
\left(
\dfrac{-4}{10}\right)^2
\\\\=
\left(
\dfrac{-2}{5}\right)^2
\\\\=
\dfrac{4}{25}
.\end{array}
Using $a^2\pm2ab+b^2=(a\pm b)^2$, then
\begin{array}{l}\require{cancel}
x^2-\dfrac{4}{5}x+\dfrac{4}{25}
\Rightarrow\left(
x-\dfrac{2}{5} \right)^2
.\end{array}
