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

Simplify the algebraic expression on the left side by distributive property
(x + 7)(x - 9) = 25
x² + 7x - 9x - 63 = 25

Then, add like-terms (the ones which have variable x)
x² + 7x - 9x - 63 = 25
x² - 2x - 63 = 25

Move the constant to the right side
x² - 2x - 63 = 25
x² - 2x = 25 + 63
x² - 2x = 88

To complete the square, we need to add 1 to both side so the left side will be in the form of complete square ⇒ x² - 2x + 1 this form is a complete square of (x - 1)
x² - 2x = 88
x² - 2x + 1 = 88 + 1
(x - 1)(x - 1) = 89
(x - 1)² = 89

Root both side


The solution
x - 1 = √89 
x = 1 + √89 

or
x - 1 = -√89
x = 1 - √89

The value of x is either 1 + √89 or 1 - √89