Solve the inequality x(x+6)>16−5x+33. Write your answer in interval notation.
First, we have to write this in standard form by combining all like terms and moving all terms to one side. We get x2+11x−49>0
Using the quadratic equation, we get x<−√317−112orx>√317−112.
Putting this into interval notation, we have (−√317−112,√317−112).
This isn't a hard problem to do. It is annoying we have square roots and an unfactorable polynomial, but not too bad in general!
Thanks! :)