169. $x^{2}+10 x=39$.

169. $x^{2}+10 x=39$. 

(Note: The equation is the same in both languages, so the translation is identical to the original text.)
169. Al-Karaji is looking for a number which, when added to $x^{2}+10 x$, would make a complete square. Such a number is 25. Then

$x^{2}+10 x+25=(x+5)^{2}=39+25=64 ; x+5=8$ and $x=3$.

He calls this method the "method of solving in the manner of Diophantus".