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