Question

Please help me!! Will get brainliest!

Answer 1

Completing the square follows the principle of taking $a x^{2} +bx+c$ and converting it into $(x+ \frac{b}{2})^2+d$ 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 $a x^{2} +b$.

In this case, 2/2=1 so we have the first part: $(w+1)^2$.
Expanding this gives us $w^2+2w+1$. We need c to be 9, so we can just add 8.
Putting this together:

$w^2+2w+9=(w+1)^2+8$

Now we can solve it more easily.
Rearranging:
$(w+1)^2=-8 \\ w+1= +-\sqrt{-8} = +-\sqrt{8}i=+-2 \sqrt{2}i \\ \boxed{w=-1+ 2\sqrt{2}i\ or\ -1-2 \sqrt{2}i }$