To solve the equation $f(x) = -9x^2 + 1.7x + 2.5 = 0$ using simple fixed-point iteration, we first rearrange it into the form $x = g(x)$.

Rewriting the equation:

We can rewrite $f(x) = -9x^2 + 1.7x + 2.5 = 0$ as: $x = g(x) = \frac{1.7x + 2.5}{9x}$

Fixed-point iteration:

Starting with $x_0 = 5$, we'll use the iterative formula: $x_{n+1} = g(x_n)$ and compute the next values up to 6 iterations.

Iterations Table:

Iteration	$x_n$	$x_{i+1}$
0	5.0000	0.2444
1	0.2444	1.3253
2	1.3253	0.3985
3	0.3985	0.8860
4	0.8860	0.5024
5	0.5024	0.7418
6	0.7418	-

After 6 iterations, the value of $x$ begins to stabilize. The method will continue to approach the root with further iterations.

Would you like to explore more iterations, or discuss the process in detail?