Number Theory GCD Linear Combination

Hi again (as you can tell, I've been working on this stuff all day, sorry for posting so much!) (Worried)

Right now I'm working on a Linear Combinations problem.

**Here's the problem: **

*Write GCD(1326,252) as a linear combination of 1326 and 252.*

**Here's what I have:**

**Find the GCD:**

1326 = 5 * 252 + 66

252 = 3 * 66 + 58

66 = 1 * 58 + 8

58 = 7 * 8 + 2

8 = 4 * 2 + 0 so 2 is the GCD

**Now work backwards:**

2 = 58 - 7 * 8

8 = 66 - 1 * 58

58 = 252 - 3 * 66

66 = 1326 - 5 * 252

**Substitute: ****this is where I'm having problems!*

2 = 58 - 7 * 8

= 58 - 7 * ( 66 - 1 * 58 )

= 8 ( 58 ) - 7 ( 66 ) **<---** but I need it in **1326,252** form, so I continue...

= 8 ( 252 - 3 * 66 ) - 7 ( 1326 - 5 * 252 )

= 8 ( 252 - 3 ( 1326 - 5 * 252 ) - 7 ( 1326 - 5 * 252 )

= 8 ( 252 ) - 24 ( 1326 - 5 * 252 ) - 7 ( 1326 ) + 35 ( 252 )

= 8(252) -24(1326) +120(252) -7(1326) +35(252)

= 163(252) -31(1326) **// simplified**

= -31(1326) +163(252) **// swapped sides**

But this equals 30 so I am messing up somewhere.

It should equal 2 right? I can't figure out where I got the +28 (Headbang)