Write the standard form of the following using completion square 25x² + 16y - 64y - 336 = 0

We are given the equation:

\[
25x^2 + 16y - 64y - 336 = 0
\]

To rewrite this equation in standard form by completing the square, let's follow these steps:

### Step 1: Group the terms with similar variables
The equation involves \(x\) and \(y\) terms, so group them accordingly:

\[
25x^2 + (16y - 64y) - 336 = 0
\]

### Step 2: Combine the like terms for \(y\)
Simplify the terms with \(y\):

\[
25x^2 - 48y - 336 = 0
\]

### Step 3: Isolate the constant
Move the constant term (-336) to the other side of the equation:

\[
25x^2 - 48y = 336
\]

### Step 4: Solve for \(x^2\)
Since there is no term to complete the square for \(y\), the equation is already simplified in standard form.

The final result is:

\[
25x^2 - 48y = 336
\]

Do you want more details on any specific step or have any questions?

Here are 5 related questions to expand your understanding:
1. How do you complete the square for a quadratic term?
2. Can this equation be represented as a conic section?
3. How can you apply similar steps to equations with higher-degree terms?
4. What happens if you have both \(x\) and \(y\) squared terms?
5. How can you manipulate equations to express them in vertex form?

**Tip:** Always check for common factors before completing the square to simplify the process.

Learn how to convert the equation 25x² + 16y - 64y - 336 = 0 into its standard form by completing the square. This step-by-step solution simplifies the quadratic expression and is suitable for students in Grades 9-10.

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