[tex] (x+b)=x^2+2bx+b^2 [/tex]
We see here that our b in this equation would be 8. That's becuase:
[tex] 2bx=16x \implies\\
bx=8x \implies\\
b=8 [/tex]
So, we need to add b^2 or 8^2 in this case to be able to complete the square, so:
[tex] x^2+16x=0 \implies \\
x^2+16x+64=64 \implies \\
(x+8)^2=0 [/tex]
We see that the number we have to add to complete the square in this problem is 64.
