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To convert the given equation from general form to standard form, we need to complete the square.

### Given Equation:
\[
x^2 + y^2 + 14x + 36 = 0
\]

### Steps to Convert:

1. **Group the \( x \) terms**:
   \[
   (x^2 + 14x) + y^2 + 36 = 0
   \]

2. **Complete the square for the \( x \) terms**:
   - Take the coefficient of \( x \), which is 14, divide it by 2, and square it:
     \[
     \left(\frac{14}{2}\right)^2 = 7^2 = 49
     \]
   - Add and subtract 49 inside the equation:
     \[
     (x^2 + 14x + 49 - 49) + y^2 + 36 = 0
     \]
   - This can be rewritten as:
     \[
     ((x + 7)^2 - 49) + y^2 + 36 = 0
     \]
   - Simplify the equation:
     \[
     (x + 7)^2 + y^2 - 13 = 0
     \]
   - Finally, move the constant to the other side:
     \[
     (x + 7)^2 + y^2 = 13
     \]

### Standard Form:
\[
(x + 7)^2 + y^2 = 13
\]

This is the equation of a circle in standard form with center \((-7, 0)\) and radius \(\sqrt{13}\).

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

### Related Questions:
1. How do you complete the square for a general quadratic equation?
2. What is the standard form of the equation of a circle?
3. How do you find the center and radius from the standard form of a circle's equation?
4. Can this process be applied to equations with different coefficients for \(x^2\) and \(y^2\)?
5. What happens if the equation of a circle is not equal to a positive number?

### Tip:
When completing the square, always remember to balance the equation by adding and subtracting the same value.

Learn how to convert a general form equation to standard form using the method of completing the square. This detailed guide covers essential mathematical concepts like completing the square, the equation of a circle, and more. Suitable for advanced high school students and college-level learners.

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