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

Did you know that the equation \( x^{2}+6x+9=0 \) is actually a perfect square trinomial? It can be factored to \( (x+3)^2=0 \). This means it has a double root, and you can solve for \( x \) simply by taking the square root, leading us to the solution \( x = -3 \). In real-world applications, understanding quadratic equations like this one can be incredibly useful! For instance, if you're calculating the area of a square garden with a side length represented by \( x + 3 \), setting this area to zero can help determine necessary modifications if the area unexpectedly shrinks to nothing. It shows how math maintains its presence in everyday scenarios!