Question

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

Answer 1

`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`