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Question

The equation - 2x ^ 2 - 12x = 12 is rewritten in the form of - 2 * (x - p) ^ 2 + q = 0 . What is the value of ? Show all work that leads to your answer.

Answer 1

Transform the required form of the expression -2 * (x - p) ^ 2 + q = 0 opening parenthesis:

-2 (x^2 - 2px + p^2) + q

-2x^2 + 4px - 2p^2 + q

It has to be the same for all values of X with the original expression - 2x ^ 2 - 12x = 12 :

-2x^2 - 12x - 12

It happens when all corresponding coefficients are equal:

-2 = -2

+4p = -12

-2p^2 + q = -12

Solving this system of equations:

p = -3

q = 6

It is called "method of undetermined coefficients"