Use completely the square to solve for x in the equation (x+7)(x-9)=25

You mean "completing the square," don't you?  ;)

(x+7)(x-9)=25 can be expanded:  x^2 - 9x + 7x - 63 + 25, which becomes

x^2 -2x = 38.

Let's now complete the square:

x^2 - 2x + (1)^2 - (1)^2 = 38, or    x^2 - 2x + 1 = 39

Rewrite that as                               (x-1)^2 = 39

Take the sqrt of both sides:              x-1 = plus or minus sqrt(39)

Write the roots:  x = 1+sqrt(39) and x = 1 = sqrt(39)         (answers)