Use simple fixed point iteration to locate the root of f(x)=-9x^2+1.7x+2.5 with initial values x=5 perform 6 iterations. Add a column for xi+1

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?

Use simple fixed point iteration to locate the root of f(x) = -9x^2 + 1.7x + 2.5 with initial values x=5, perform 6 iterations. Add a column for xi+1.

Solve the quadratic equation f(x) = -9x^2 + 1.7x + 2.5 using simple fixed point iteration. This problem demonstrates key numerical methods concepts with step-by-step iterations, making it suitable for advanced high school or undergraduate students.

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