2x 2 +5x-12

2x² + 5x - 12

= 2 (x² + 5x/2 - 6)

= 2 (x² + 5x/2 + 25/8 - 73/8)

= 2(x + 5/4)² - 73/4

= (2x + 2.5)² - 73/4

= \((2x + \dfrac{5}{2}-\dfrac{1}{2}\sqrt{73})(2x+\dfrac{5}{2}+\dfrac{1}{2}\sqrt{73})\)

Whoops what am I doing

I should do:

\(2x^2 + 5x - 12 = 0\\ x = \dfrac{-5 \pm \sqrt{5^2-4(2)(-12)}}{2(2)}\\ \;\;=\dfrac{-5\pm 11}{4}\\ x = \dfrac{3}{2}\text{ OR }-4\\ \therefore 2x^2 + 5x - 12 = (2x - 3)(x + 4)\)