Your equation is
[tex] (x-8)^2 = 7 [/tex]
So, you're asking that the left hand side, squared, must be 7.
There are only two possibilities for a number to give 7 then squared: that number is even the square root of 7 or its opposite.
So, one solution is given by [tex] x-8 = \sqrt{7} \implies x = 8+\sqrt{7} [/tex].
The other is given by [tex] x-8 = -\sqrt{7} \implies x = 8-\sqrt{7} [/tex].
