Question

please solve for t by hand: (0.133t^3)-(2t^2)=-10.47

the answer is t=2.51s but I am unsure how to get there.

Answer 1

We have (0.133t³)-(2t²) = -10.47 or, (0.133t³)-(2t²)+10.47 =0. This is a cubic equation which will have 3 roots. The best way is to sketch a graph. A graph of f(t) =(0.133t³)-(2t²)+10.47, using a graphing calculator is attached. It may be observed that the graph crosses the X-Axis at x = -2.141,x = 2.506 and x = 14.672. Hence the answer is t = -2.141, 2.506 or, 14.672.

Note:

It is difficult to solve a cubic equation by hand, especially when it does not have integral coefficients. The best way is sketch a graph.

The exact coordinates may be seen in the original desmos graph and not in an image thereof.