I have a question that requires me to solve by completing the square but leave the answers in SURD form:

I have got as far as the following:

x^2+8x+10=0

x^2+8x+10=(x-4)^2-4^2+10

(x-4)^2-16+10

(x-4)^2-6=0

(x-4)^2=6

x-4=√6 or -√6

x=4√6 or -4√6

Now I think this is wrong I just don't know what steps are missing or at what point i have made a mistake?

Any help is appreciated.

Thanks in advance.