How do you solve #18x^2+10x=-3x+21#?

1 Answer
May 26, 2017

Answer:

#7/9 and - 3/2#

Explanation:

Use the new Transforming Method (Socratic Search):
#y = 18x^2 + 13x - 21 = 0#
Transformed equation: #y' = x^2 + 13x - 378 = 0#
Method: Find 2 real roots of y', then, divide them by a = 18.
Compose factor pairs of (ac = - 378), using a calculator.
...(6 - 18)(7, - 34)(14, - 27). This last sum is (-13 = - b). Then, the 2 real roots of y' are: 14 and - 27.
Back to y, its 2 real roots are:
#x1 = 14/a = 14/18 = 7/9#, and #x2 = -27/a = -27/18 = - 3/2#
Answers: #7/9 and - 3/2#