discrete mathematics - Extended euclidean algorithm

So I am trying to figure this out.
And for one of the problem the question is x*41= 1 (mod 99)
And the answer lists

 x | 41x mod 99
 0    99
 1    41

 -2   17
 5    7
 -12  3
 29   1

And conclude x=29

How did they get this value(can someone explain)? To better put, how do you calculate this?