+823 Solve the inequality $4t^2 \le -9t + 12 - 14t + 36.$ Write your answer in interval notation.
+130071 4t^2 ≤ -9t + 12 -14t + 36 simplify as
4t^2 + 23t -48 ≤ 0 set as an inequaity
4t^2 + 23t - 48 = 0 use the quadratic formula to find the roots
[ -23 +/- sqrt [ 23^2 - 4*4*-48 ] / (2*4) = t
[-23 +/- sqrt [ 1297 ] / 8 = t
This is a parabola which intersects the x axis....the part lying between the roots will be the answer
So....the solution is
[ -23 - sqrt 1297 ] /8 ≤ t ≤ [ -23 + sqrt 1297] / 8
