To solve the equation $x^2 + 4x = 12$ by completing the square, we’ll follow these steps:

1. Rewrite the equation in standard form for completing the square: $x^2 + 4x = 12$

2. Move the constant term to the other side: $x^2 + 4x - 12 = 0$ But here, for completing the square, it’s often more convenient to isolate the terms involving $x$: $x^2 + 4x = 12$

3. Complete the square for the expression $x^2 + 4x$: To complete the square, take half of the coefficient of $x$, square it, and add it to both sides:

   • Half of 4 is 2, and $2^2 = 4$.

   So, add 4 to both sides: $x^2 + 4x + 4 = 12 + 4$ $(x + 2)^2 = 16$

4. Take the square root of both sides: $x + 2 = \pm 4$

5. Solve for $x$:

   • If $x + 2 = 4$, then $x = 2$.
   • If $x + 2 = -4$, then $x = -6$.

So, the solutions are: $x = -6 \text{ and } x = 2$

Answer: The correct option is $x = -6$ and $x = 2$.

Would you like a more detailed explanation of the steps involved?

Here are some related questions to further your understanding:

1. How do you determine what number to add when completing the square?
2. What is the significance of taking the square root on both sides after completing the square?
3. Can completing the square method be applied to any quadratic equation?
4. How does completing the square relate to finding the vertex of a parabola?
5. Are there alternative methods to solve quadratic equations aside from completing the square?

Tip: Completing the square is particularly useful for converting a quadratic equation into vertex form, which can help in graphing parabolas.