An engineering problem (related to airplane engines) involves solving (with respect to x)

x^6 - 27*x^5 + 105*x^4 - 104*x^3 + 81*x^2 - 21*x + 2 = 0

We can draw the graph with JavaScript; for example by this **script**:

I understand that there is a solution between 0 and 10 and there is another between 10 and 25.

By using**
equp2.htm**:

a = 0 b = 10 ...

a = 3.4443262222098245 b = 3.444326222209825

a = 10 b = 25 ...

a = 22.539168743888883 b = 22.539168743888887

The solutions are 3.44432622220982 and 22.53916874388888 (but we can be satisfied with a smaller number of digits).

We could do without drawing the graph. We could identify the initial intervals in which the solutions fall by using the** [test] **button.

[the problem is taken from "Science with Pocket Calculators" by David R. Green, John L. Lewis (1978)]