The image presents an iterative method to approximate the solution to the equation $x^3 - 5x^2 - 12 = 0$. The instructions given are as follows:

1. Step 1: Start with an initial value of $x$.
2. Step 2: Calculate the value of $5 + \frac{12}{x^2}$.
3. Step 3: Compare the rounded value of the result from Step 2 and $x$ (both rounded to 2 decimal places). If they are the same, you have found an approximate solution. If not, use the new value from Step 2 as the new $x$ and repeat.

This is essentially a fixed-point iteration method, often used for solving equations numerically. The formula $x = 5 + \frac{12}{x^2}$ comes from rearranging the original equation in a way that facilitates iteration.

Would you like to work through an example or need further details on how this method works?

Here are five follow-up questions that might expand on this topic:

1. What are other numerical methods for solving cubic equations?
2. How does the convergence of this method compare to other iteration methods, like Newton-Raphson?
3. What is the significance of rounding to two decimal places in this method?
4. How would the method perform if a poor initial guess for $x$ was chosen?
5. How could you check if a solution to $x^3 - 5x^2 - 12 = 0$ is accurate?

Tip: Always check that your iteration method converges to a solution, as some choices of starting values can lead to divergence.