Answer
$\displaystyle \{\frac{4}{5}\}$
Work Step by Step
Write in standard form (subtract 40x from both sides)
$25x^{2}-40x+16=0$
$25x^{2}=(5x)^{2}$,
$16=(4)^{2}$
$2\cdot 5x\cdot 4=40x$,
so, we recognize a perfect square on the LHS
$(5x-4)^{2}=0\Rightarrow 5x-4=0$
$5x=4$
$x=\displaystyle \frac{4}{5}$
Solution set = $\displaystyle \{\frac{4}{5}\}$
