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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.​

Respuesta :

Given:

The equation for the area of the first option is:

[tex]x^2+200x=166400[/tex]

Where x is the side length of the current square park.

To find:

The side length of the current square park.

Solution:

We have,

[tex]x^2+200x=166400[/tex]

It can be written as:

[tex]x^2+200x-166400=0[/tex]

Splitting the middle term, we get

[tex]x^2+520x-320x-166400=0[/tex]

[tex]x(x+520)-320(x+520)=0[/tex]

[tex](x-320)(x+520)=0[/tex]

[tex]x=320,-520[/tex]

We know that the side length of a park cannot be negative. So, the only possible value of x is 320.

Therefore, the most direct method to solve the given equation is splitting the middle term and the side length of the current square park is 320 meters.

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