Given : x² + 200x = 166400 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 To Find : the side length of the current square park. Solution: x² + 200x = 166400 => x(x + 200) = 166400 166400 = 320 * 520 => (320)(320 + 200) = 166400 => x = 320 side length of the current square park. = 320 m Learn More: Which expression is a possible leading term for the polynomial ...

320 m

Explanation:

To find the side length of the current park, x, we solve the quadratic equation for the area of the park

x² + 200x = 166400

x² + 200x - 166400 = 0

We multiply -166400 by x² to get -166400x². We now find the factors of 166400x² that will add up to 200x. These factors are -320x and 520x

So, we re-write the expression as

x² + 200x - 166400 = 0

x² + 520x - 320x - 166400 = 0

We write out the factors of the expression,

x² + 520x - 320x - 320 × 520 = 0

Factorizing the expression, we have

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

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

x + 520 = 0 or x - 320 = 0

x = -520 or x = 320

Since x is not negative, we take the positive answer.

So, x = 320 m

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