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The question asks you to solve the quadratic equation \( x^2 + 6x = -8 \) by completing the square, and to choose the correct process for rearranging the equation to obtain a form of \( (x + k)^2 = d \).

### Completing the Square Process

1. **Start with the given equation**:
   \[
   x^2 + 6x = -8
   \]
   
2. **Move the constant term to the other side**:
   \[
   x^2 + 6x + \_ = -8 + \_
   \]
   We will add a term to both sides to complete the square on the left-hand side.

3. **Find the term to complete the square**:
   Take half of the coefficient of \(x\), square it, and add it to both sides:
   \[
   \left(\frac{6}{2}\right)^2 = 9
   \]
   Add 9 to both sides:
   \[
   x^2 + 6x + 9 = -8 + 9
   \]
   Simplifying the right-hand side:
   \[
   x^2 + 6x + 9 = 1
   \]

4. **Factor the left-hand side**:
   The left-hand side is now a perfect square trinomial:
   \[
   (x + 3)^2 = 1
   \]

This matches the form \( (x + k)^2 = d \), where \( k = 3 \) and \( d = 1 \).

### Analyzing the Answer Choices:

Looking at the options provided in the image, **Option A** is the correct one:

\[
x^2 + 6x = -8 \implies x^2 + 6x + 9 = -8 + 9
\]

Would you like further details or have any questions?

Here are 5 related questions to further your understanding:
1. How does completing the square help in solving quadratic equations?
2. What are other methods to solve quadratic equations besides completing the square?
3. Why do we take half of the coefficient of \(x\) when completing the square?
4. What would the solution be if you solved \( (x+3)^2 = 1 \)?
5. Can you complete the square for a quadratic equation where the coefficient of \(x^2\) is not 1?

**Tip**: When completing the square, always ensure that the coefficient of \(x^2\) is 1 before applying the method. If it's not, factor it out from the whole equation.

Solve the quadratic equation by completing the square: x^2 + 6x = -8.

This page explains how to solve the quadratic equation x^2 + 6x = -8 by completing the square, including step-by-step instructions for finding the solution and understanding the method of completing the square. Suitable for students in Grades 8-10.

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