To solve the equation $f(x) = -9x^2 + 1.7x + 2.5 = 0$ using simple fixed-point iteration, we need to rewrite the equation in the form $x = g(x)$. Let's isolate $x$ to set up the iteration formula.

We can rearrange the equation as follows:

$x = g(x) = \frac{1.7x + 2.5}{9x}$

For simplicity, we'll now start the fixed-point iteration method:

Steps for Fixed-Point Iteration:

1. Choose an initial guess for $x_0$. Given $x_0 = 5$.
2. Use the function $g(x)$ to calculate the next $x$ value: $x_{n+1} = g(x_n)$
3. Repeat the process until the values converge.

Let's compute the first few iterations manually:

Iteration 1:

Using $x_0 = 5$: $x_1 = g(x_0) = \frac{1.7(5) + 2.5}{9(5)} = \frac{8.5 + 2.5}{45} = \frac{11}{45} \approx 0.2444$

Iteration 2:

Now, using $x_1 = 0.2444$: $x_2 = g(x_1) = \frac{1.7(0.2444) + 2.5}{9(0.2444)} = \frac{0.41548 + 2.5}{2.1996} \approx 1.3242$

Iteration 3:

Using $x_2 = 1.3242$: $x_3 = g(x_2) = \frac{1.7(1.3242) + 2.5}{9(1.3242)} = \frac{2.25114 + 2.5}{11.918} \approx 0.3779$

Iteration 4:

Using $x_3 = 0.3779$: $x_4 = g(x_3) = \frac{1.7(0.3779) + 2.5}{9(0.3779)} = \frac{0.64243 + 2.5}{3.4011} \approx 0.921$

The process will continue until convergence (when $|x_{n+1} - x_n|$ is sufficiently small).

Would you like me to continue more iterations, or would you like a detailed explanation of each step?