(h) \( \quad(x-2)^{2}=16 \)

Let's dive into the world of equations! This equation, \( (x-2)^{2} = 16 \), is an example of a quadratic equation. It's super fun because you can solve it by taking the square root of both sides. Doing so, you get \( x-2 = 4 \) or \( x-2 = -4 \). This leads to two possible solutions: \( x = 6 \) or \( x = -2 \). Who knew math could be this thrilling? Now, let’s put this into some real-world context! Imagine you're designing a small park and want to create a perfect square picnic area that covers an area of 16 square units. The distance from the center to a side of the picnic area (which represents \( x-2 \)) can be adjusted. By solving the equation, you determine that the center should be positioned at either coordinate \( x=6 \) (for more space) or \( x=-2 \) (for a cozy corner). You're now armed with a mathematical way to design the perfect outing!