How do you solve 2x²-17x=9?

Aug 5, 2016

-1/2 and 9

Explanation:

Solving by the new Transforming Method (Socratic Search).
$y = 2 {x}^{2} - 17 x - 9 = 0$
Transformed equation: $y ' = {x}^{2} - 17 x - 18 = 0$
Method. Find the 2 real roots of y', then divide them by a = 2.
Since a - b + c = 0, use shortcut. Two real roots are: -1 and $- \frac{c}{a} = 18$.
Back to original equation y --> its 2 real roots are: $x 1 = - \frac{1}{2}$ and
$x 2 = \frac{18}{2} = 9$.