Ann works for a city’s parks and recreation department. She is looking for some commercial land to rezone for recreational use and has found two possible options.
Part A
Ann’s first option is a plot of land adjacent to a current park. The current park is a square, and the addition will increase the width by 200 meters to give the expanded park a total area of 166,400 square meters. This equation represents the area of the first option, where x is the side length of the current square park:
x2 + 200x = 166,400.
Use the most direct method to solve this equation and find the side length of the current square park. Explain your reasoning for both the solving process and the solution.