I'm working a problem in my textbook and am stuck. Here's what I have so far:

GCD (34, 58)

58 = 34 x 1 + 24

34 = 24 x 1 + 10

24 = 10 x 2 + 4

10 = 4 x 2 + 2 = GCD (4, 2)

So working backwards:

2 = 10 - 4 x 2

= 10 - (24 - 10 x 2) x 2

= 10 x 2 - 24 + 10 x 2

= 10 x 4 - 24

= (34 - 24) x 4 - 24

And that's where I get lost. I work it through and cannot seem to get the right answer. I know that I need to get 12 to go with a and 7 to go with b, but how do I express this going backwards using the algorithm? There must be some mistake I'm making. Thanks in advance