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)