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The equation provided in the general form is:

\[
9x^2 - 4y^2 - 36x + 24y - 36 = 0
\]

We need to convert this to the standard form for hyperbolas, which looks like:

\[
\frac{(x - E)^2}{G} - \frac{(y - F)^2}{H} = 1
\]

### Step 1: Rearranging and Grouping Terms
First, group the \(x\) and \(y\) terms together:

\[
9(x^2 - 4x) - 4(y^2 - 6y) = 36
\]

### Step 2: Completing the Square
We will complete the square for both the \(x\) and \(y\) terms.

#### For the \(x\) terms:
The expression inside the parentheses is \(x^2 - 4x\).
To complete the square, take half of \(-4\) (which is \(-2\)), square it (\((-2)^2 = 4\)), and add and subtract this value:

\[
9(x^2 - 4x + 4 - 4) = 9((x - 2)^2 - 4)
\]

This simplifies to:

\[
9(x - 2)^2 - 36
\]

#### For the \(y\) terms:
The expression inside the parentheses is \(y^2 - 6y\).
Take half of \(-6\) (which is \(-3\)), square it (\((-3)^2 = 9\)), and add and subtract this value:

\[
-4(y^2 - 6y + 9 - 9) = -4((y - 3)^2 - 9)
\]

This simplifies to:

\[
-4(y - 3)^2 + 36
\]

### Step 3: Substitute Back Into the Equation
Substitute these expressions back into the original equation:

\[
9(x - 2)^2 - 36 - 4(y - 3)^2 + 36 = 36
\]

Simplify:

\[
9(x - 2)^2 - 4(y - 3)^2 = 36
\]

### Step 4: Divide by 36 to Normalize the Equation
To get the standard form, divide the entire equation by 36:

\[
\frac{9(x - 2)^2}{36} - \frac{4(y - 3)^2}{36} = \frac{36}{36}
\]

This simplifies to:

\[
\frac{(x - 2)^2}{4} - \frac{(y - 3)^2}{9} = 1
\]

### Step 5: Identify the Constants
Now that we have the equation in standard form, we can identify the values of \(E\), \(F\), \(G\), and \(H\):

\[
E = 2, \quad F = 3, \quad G = 4, \quad H = 9
\]

Would you like further details or have any questions? 

Here are 5 related questions for further exploration:
1. How do you complete the square for any quadratic expression?
2. What does the standard form of a hyperbola represent geometrically?
3. How can you distinguish between an ellipse and a hyperbola from the general equation?
4. Why is it necessary to divide the final equation by 36 in this problem?
5. What are the key characteristics of a hyperbola's asymptotes?

**Tip:** Completing the square is a key algebraic technique for converting quadratic expressions to vertex form. Always remember to add and subtract the same value inside the parentheses.

Convert from general form to standard form.

General Form: 9x^2 - 4y^2 - 36x + 24y - 36 = 0

Standard Form: (x - E)^2 / G - (y - F)^2 / H = 1

Learn how to convert the equation 9x^2 - 4y^2 - 36x + 24y - 36 = 0 from general form to the standard form of a hyperbola. This problem involves algebra, conic sections, and completing the square. The solution provides a step-by-step guide to rewriting the equation and identifying key constants for standard form.

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