Answer
$\frac{4}{25}$; $(x+\frac{2}{5})^2$
Work Step by Step
To complete the square, add a term that is the square of half the coefficient of $x$ in the middle term. Then factor by trial and error.
$x^2+\frac{4}{5}x$
$(\frac{\frac{4}{5}}{2})^2 = (\frac{4}{5}\times\frac{1}{2})^2=(\frac{2}{5})^2 = \frac{4}{25}$
$x^2+\frac{4}{5}x+\frac{4}{25}$
$(x+\frac{2}{5})^2$
