Question

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

Answer 1

Answer:

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