The given equation is:

$\sqrt{x^2 + 6x + 9} = 0$

To solve this, follow these steps:

Step 1: Eliminate the square root

Square both sides of the equation to remove the square root:

$(\sqrt{x^2 + 6x + 9})^2 = 0^2$

This simplifies to:

$x^2 + 6x + 9 = 0$

Step 2: Factor the quadratic equation

The equation $x^2 + 6x + 9 = 0$ is a perfect square trinomial and can be factored as:

$(x + 3)^2 = 0$

Step 3: Solve for $x$

Now, solve the equation:

$x + 3 = 0$

Subtract 3 from both sides:

$x = -3$

Final Answer:

The solution is:

$x = -3$

Do you want more details or have any questions?

Here are 5 related questions:

1. How do you solve quadratic equations using the quadratic formula?
2. What is the discriminant of a quadratic equation and how does it help determine the number of solutions?
3. Can all quadratic equations be factored? Why or why not?
4. What are the properties of a perfect square trinomial?
5. How does completing the square help in solving quadratic equations?

Tip: Always check if a quadratic can be factored easily before using more complex methods like the quadratic formula!