What is the exact solution to the equation \( (x+4)^{2}-16=-4 \) ? \( x=2 \sqrt{3} \) \( x=4 \sqrt{3} \) \( x=2 \pm 1 \sqrt{3} \) \( x=-2 \pm 1 \sqrt{3} \) \( x=6 \sqrt{3} \) \( x= \pm 4 \) \( x=-4 \pm 2 \sqrt{3} \) \( x=4 \pm 2 \sqrt{3} \) \( x= \pm 2 \sqrt{3} \) \( x= \pm 2 \)

To solve the equation \( (x+4)^{2}-16=-4 \), we first simplify it. Rearranging gives us \( (x+4)^{2} = 12 \). Taking the square root of both sides leads to \( x+4 = \pm 2\sqrt{3} \). Solving for \( x \) gives us \( x = -4 \pm 2\sqrt{3} \), which matches one of your options! If we apply this in a real-world context, finding the value of \( x \) could represent a physical phenomenon, like the position of an object in a parabolic path. The ability to bridge algebra and geometry showcases the practical power of math in analyzing movement, such as a ball thrown from a height or the trajectory of a rocket. Math isn't just numbers—it's a tool to explore and understand the world around us!