Question

WILL MARK BRAINIEST, QUESTION IS HARD, 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. 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.

Answer 1

Answer:

$x =320$

Step-by-step explanation:

Given

$x^2 + 200x = 166400$

Required

Find x

We have:

$x^2 + 200x = 166400$

Rewrite as:

$x^2 + 200x - 166400 = 0$

Expand

$x^2 + 520x - 320x - 166400 = 0$

Factorize

$x(x + 520) - 320(x + 520)= 0$

Factor out x + 520

$(x - 320) (x + 520)= 0$

Split

$x - 320 = 0\ or\ x + 520= 0$

Solve

$x = 320\ or\ x =- 520$

Side length must be positive;

So:

$x = 320$