LOL you don't know your own math. The -1 you did was just to switch from negative to positive because you subtracted 3 from both sides instead of just adding the square root. Has nothing to do with the square root result you need to be -5.
Edit: Showing work:
3 - square root of (2x + 2) =8 Add square root of 2x+2 to both sides =
3 = 8 + SQR(2x + 2) -8 from both sides =
-5 = SQR(2x + 2) square both sides =
25 = 2x +2 -2 both sides =
23 = 2x /2 both sides =
11.5 = x
When you do the check it works with the negative root, -5, but not with the positive root, 5. So you have to specify which root in the initial equation notation or it's not a valid equation right?