<PRE><B>Question 340564</B>
30x^2 + 11x - 30 = 0



Here we have to make +30 and -30 into factors so that juggling cross products will give a sum of 11.


5 and 6 are the two most likely answers as when added up give 11 which is the difference of the two squares (36 - 25).


This we need (6x with 5) and (5x with 6) so that we have 30x^2 and -30. The -30 tells us there is a minus and so the sum (11) can be treated as a difference.


(6x with 5)(5x with 6) = 30x^2 + (36 with 25)x + (5 with 6)


(6x - 5)(5x + 6) = 30x^2 + (36 - 25)x + (-5 times 6) = 30x^2 + 11x - 30 = 0


6x - 5 = 0 and 5x + 6 = 0



Giving x = 5/6 and -1.2</PRE>