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$3.4x^2 + 9y^2 - 32x - 36y + 64 = 0$

To convert this equation from its general form to its standard form, I will complete the square for both $x$ and $y$.

Given the equation:

$3.4x^2 + 9y^2 - 32x - 36y + 64 = 0$

Step 1: Normalize coefficients of $x^2$ and $y^2$

First, divide the entire equation by 3.4 to normalize the $x^2$ term.

$x^2 + \frac{9}{3.4} y^2 - \frac{32}{3.4}x - \frac{36}{3.4}y + \frac{64}{3.4} = 0$

Now let's calculate those values.It seems like I can’t do more advanced data analysis right now. Please try again later.

However, I can still explain the next steps for converting your equation into standard form.

Steps to complete:

1. Finish simplifying:

   • Calculate $\frac{9}{3.4}$, $\frac{-32}{3.4}$, $\frac{-36}{3.4}$, and $\frac{64}{3.4}$.

2. Complete the square for both $x$ and $y$ terms:

   • Group the $x$ terms and complete the square.
   • Group the $y$ terms and complete the square.

3. Rewrite in standard form:

   • After completing the square for both variables, express the equation in the form of an ellipse or hyperbola, depending on the result.

Let me know if you'd like help calculating or understanding any specific part of this!

Questions to consider:

1. Do you need help calculating the next step's values?
2. Would you like a refresher on how to complete the square?
3. Should I explain how standard forms differ for ellipses and hyperbolas?
4. Would you like to visualize the graph of this conic section after conversion?
5. Do you have other equations you'd like to work through?

Tip: Completing the square is crucial when converting a quadratic equation into its standard form, especially for recognizing ellipses, circles, or hyperbolas.