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The equation provided is in standard form for a circle:

\[
(x + 7)^2 + y^2 = 13
\]

To convert this to the general form, we need to expand the equation and rearrange it. Let's go through the steps:

1. **Expand the square term**:
   \[
   (x + 7)^2 = x^2 + 14x + 49
   \]

2. **Substitute the expanded form into the equation**:
   \[
   x^2 + 14x + 49 + y^2 = 13
   \]

3. **Move all terms to one side to set the equation equal to 0**:
   \[
   x^2 + 14x + y^2 + 49 - 13 = 0
   \]

4. **Simplify the constants**:
   \[
   x^2 + y^2 + 14x + 36 = 0
   \]

So, the general form of the equation is:

\[
x^2 + y^2 + 14x + 36 = 0
\]

Would you like any more details on this process or have any questions?

Here are some related questions you might find helpful:
1. How do you find the center and radius of a circle given its equation in general form?
2. How do you complete the square to convert from general form to standard form?
3. What is the significance of the coefficients in the general form of a circle's equation?
4. How can you graph a circle given its equation in standard form?
5. How do you identify whether an equation represents a circle, a parabola, or an ellipse?

**Tip**: When converting between standard and general forms, always keep track of constant terms carefully to avoid errors during simplification.

Learn how to convert a circle equation from standard form to general form with detailed steps. This problem covers circle equations, quadratic equations, and algebraic manipulation. Suitable for high school students in Grades 10-12.

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