Solve the inequality 4t^2 \le -9t + 12 - 4t + 23 + (2t - 1)(2t + 1). Write your answer in interval notation.
First, let's simplify the right hand side of the equation a little bit.
We get that −9t+12−4t+23+4t2−1=−13t+4t2+34
Now, we simply move all terms to one side. Note that most terms cancel out.
we get the equation
13t−34≤0
Solving for t, we get
13t≤34t≤3413
In interval notation, this is
(−inf,3413]
Thanks! :)