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

x = - 4 or 6

O O

x = - 2 or 14

X=1789

X=1187

O

x = 1 ±√89

Step-by-step explanation:

We have the equation:

(x+7) (x-9) = 25

Using distributive property:

x (x-9) + 7 (x-9) = 25

x² - 9x + 7x - 63 - 25 = 0

x² - 2x - 88 = 0

To complete squares we need to add and subtract 1, as follows:

x² - 2x - 88 + 1 - 1 = 0

x² - 2x + 1 - 88 - 1 = 0 (this is a perfect square)

(x - 1) ² - 89 = 0

Solving for x:

(x - 1) ² = 89

x - 1 = ±√89

x = 1 ±√89