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To solve this problem, we need to complete the square for the given quadratic equation \( x^2 + 6x - 3 = 0 \) and match it with one of the answer choices.

### Step 1: Start with the equation
\[
x^2 + 6x - 3 = 0
\]

### Step 2: Move the constant term to the other side
\[
x^2 + 6x = 3
\]

### Step 3: Complete the square
1. Take half of the coefficient of \( x \), which is 6. Half of 6 is 3.
2. Square this result: \( 3^2 = 9 \).
3. Add 9 to both sides to maintain the equality.

\[
x^2 + 6x + 9 = 3 + 9
\]

This simplifies to:
\[
(x + 3)^2 = 12
\]

### Step 4: Write the equation in the required form
The equivalent equation is:
\[
(x + 3)^2 - 12 = 0
\]

### Conclusion
The correct answer is:
\[
\boxed{(x + 3)^2 - 12}
\]

Would you like more details on any of the steps?

### Related Questions
1. What is the process of completing the square in more detail?
2. How can we use completing the square to solve any quadratic equation?
3. How can we verify that two quadratic equations are equivalent?
4. How does completing the square relate to the vertex form of a quadratic?
5. What other methods can be used to solve quadratic equations?

**Tip:** When completing the square, always ensure you add the same value to both sides to keep the equation balanced.

Select the equation that is equivalent to x^2 + 6x - 3 = 0

Learn how to solve the equation x^2 + 6x - 3 = 0 by completing the square. This step-by-step guide covers key algebra concepts, including rewriting the equation in vertex form. Ideal for high school algebra students.

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