jmc

First of all, we calculate that the length of $\overline{DC}$ is $17.8-5=12.8$. Since triangles $ADB$ and $BDC$ are similar, $BD/AD$ is equal to $CD/BD$, giving us the equation $x/5=12.8/x$. Multiplying both sides by $5x$, we get $x^2=64$, so $x=\boxed{8}$ units.