Here are your fill-ins:
r = 1 is a zero, so (r-1) is a factor.
r = -1 is a zero, so (r+1) is a factor.
The remainders from synthetic division are 0 each time.
See the attachment for the synthetic division numbers.
_____
The reduced quadratic is ...
... x² -6x +13 = 0
Solving by completing the square, we have ...
... (x -3)² = -4
... x = 3 ± 2i
_____
The quadratic formula would tell you ...
... x = (-(-6) ± √((-6)² -4(1)(13)))/(2·1) = (6±√-16)/2 = 3±2i
