How to make use of completing the square to solve for x in the equation (x + 7)(x - 9) = 25

It is a standard practice to learn the formula for x that is derived from a quadratic expression.

Answer: The result of the solution gives x = ±  √89 + 1 .

Solving a quadratic function whose R.H.S is a non-zero number may shift the zeros of the initial quadratic, mentioned on the L.H.S.

Explanation:

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

Simply the equation into a proper form to complete the square.

⇒ x² - 2x - 63 = 25

⇒ x² - 2x = 88

To create a trinomial square on the left side of the equation, find a value that is equal to the square of half of b.

(b / 2)² = (-1)²

Add the term to each side of the equation

⇒ x² - 2x + (-1)² = 88 + (-1)² 

⇒ x² - 2x + 1 = 89

Factor the perfect trinomial square into (x - 1)²

⇒ (x - 1)² = 89

Taking square root for both the sides and solving the equation for x

⇒ x = ±  √89 + 1

Hence, the result of the solution gives x = ±  √89 + 1.