Question

(x-7)^2=0 does this have a real solution?

Answer 1

yes that does have a solution if u replace x with 7 your solution will be 0, because
(7-7)^2=0
(0)^2=0
0=0

Answer 2

Yes. You can solve in the usual way.

Take the square root:

... x-7 = ±√0 = 0

Add 7:

... x = 7

_____

There is one distinct real solution (with multiplicity 2).