you are basically at this point:
a^2+b^2=c^2
(10+x)^2=625-49
(10+x)^2=576
if you have not learned formulas to solve quadratic equations directly you can also "just" take the square root of both sides:
you have to remember that there are always two possiblites when finding a root: -a*-a=a^2 and a*a=a^2
(this is possibly your "factoring" hint)
so if you take the squareroot on both sides you get:
+/-(10+x)=+/-24
you know 24 has to be positive as it is the length of one side of the triangle
+/-(10+x)=24
2 solutions/equalities:
10+x=24
x=14
and
-10-x=24
-x=34
x=-34
obviously x+10>0 must hold true as your triangle side can only have a positive length, similar to 24 previously this leaves you only with x=14, because otherwise it would be 10-34<0
so x=14
This solution doesn't use the usual factoring as the hints seem to suggest, but instead for the squareroot
you might be supposed to find a slightly different way for the resolution in the end, but I didn't find it yet :)
