Completing the square confusing me

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.

Another way of going about it

Fortunately your starting equation is in standard form so just follow these steps:

1) Move the ten to the other side to get:

x^2 + 8x = -10

2) Take 1/2 of the number in the 8x term, square it, then add the result to both sides which yields:

x^2 + 8x + 16 = -10 + 16 = 6

3) Now factor out the left-hand side to get:

(x + 4)^2 = 6

Can you proceed from here on?