How do you solve #12x ^ { 2} - 4x + 16= 952#?

1 Answer
Nghi N
Mar 13, 2018

#- 26/3#, and 9

Explanation:

#12x^2 - 4x + 16 = 954#
Divide both sides by 4 -->
#3x^2 - x + 4 = 238#
#3x^2 - x - 234 = 0#
Next, solve the quadratic equation by the New Transforming Method (Socratic Search)
#y = 3x^2 - x - 234 = 0#
Transformed equation:
#y' = x^2 - x - 702 = 0. #
Proceeding. Find 2 real roots of y', then, divide them by a = 3.
Find 2 real roots knowing the sum (- b = 1) and the product
(c = -702). They are: (-26) and (27).
Back to y, the 2 real roots are:
#x1 = -26/a = -26/3 , and x2 = 27/3 = 9

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