Solve the inequality $x(x + 6) > 16 - 5x + 33.$ Write your answer in interval notation.

LiIIiam0216 May 22, 2024

#1**0 **

First, we have to write this in standard form by combining all like terms and moving all terms to one side. We get \(x^2+11x-49>0\)

Using the quadratic equation, we get \(x<\frac{-\sqrt{317}-11}{2}\quad \mathrm{or}\quad \:x>\frac{\sqrt{317}-11}{2}\).

Putting this into interval notation, we have \((\frac{-\sqrt{317}-11}{2}, \frac{\sqrt{317}-11}{2})\).

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! :)

NotThatSmart May 23, 2024