How do you solve # 14-5x-x^2<0#?
Just to make things easier, we multiply both sides by
We factorize the expression:
These are the only two possible points where the expression can change signs. Thus, there are three regions that have the same sign:
#x<-7# #-7 < x < 2# #x>2#
Since there are no repeated roots, the signs of the region alternate. We substitute an arbitrary number in the second region to find the sign:
Therefore, the first and third regions are positive (you can use substitution to be sure). Looking at the inequality,
The solution is the first and third regions: