Completing the square follows the principle of taking [tex]a x^{2} +bx+c[/tex] and converting it into [tex](x+ \frac{b}{2})^2+d [/tex] where d is the 'correctional number' as I like to call it - i.e. the number that converts the expanded bracket into the +c, since the expanded bracket will give us [tex]a x^{2} +b[/tex].
In this case, 2/2=1 so we have the first part: [tex](w+1)^2[/tex].
Expanding this gives us [tex]w^2+2w+1[/tex]. We need c to be 9, so we can just add 8.
Putting this together:
[tex]w^2+2w+9=(w+1)^2+8[/tex]
Now we can solve it more easily.
Rearranging:
[tex](w+1)^2=-8 \\ w+1= +-\sqrt{-8} = +-\sqrt{8}i=+-2 \sqrt{2}i \\ \boxed{w=-1+ 2\sqrt{2}i\ or\ -1-2 \sqrt{2}i }[/tex]
