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Solving Quadratic Equations

A person plants two square plots for garden. the of the areas of both plots is 225 square feet. If the side of one plot is 3 feet longer than the side of the other one, find the length of the smaller plot.

Karin Algebra Class Says:

Let x = the side of the smaller plot.

Since the other plot is 3 feet longer, the second plot's length is x +3.

You know the area of the both plots is 225.

Therefore, we need to find the area of both plots and add them together to get 225.

Remember area of a square is s^2 or the side squared.

Plot 1 area + Plot 2 area = 225
x^2 + (x+3)^2 = 225

x^2 + x^2 + 6x + 9 = 225


2x^2 + 6x + 9 = 225

Now, set the equation equal to 0 by subtracting 225 from both sides.

2x^2 + 6x + 9 - 225 = 225 - 225

2x^2 + 6x -216 = 0

Now use the quadratic formula to solve.

a = 2, b = 6, c = -216

Use the following web page for examples on how to use the quadratic formula:


Your answer should end up to be 9 for the length of the shorter plot.

Good luck,

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Dec 10, 2010
Solving Quadratic Equations
by: Karin

In order to multiply (x+3)^2, you can use the foil technique.

First distribute the first x throughout the second parenthesis:

Multiply x * x to get x^2
Multiply x * 3 to get 6x

Then distribute the 3 throughout the second parenthesis:

Multiply 3*x to get 3x
Multiply 3*3 to get 9.

Then combine 3x + 3x to get 6x

So you end up with
x^2 + 6x + 9

Since I can't use graphics in this application it is very difficult to explain in words. Take a look at the lesson on foil and it might help to explain this more clearly.


I hope this helps,

Dec 10, 2010
by: Anonymous

Sorry I was woundering how you got 9
right here 2X^2+6X+9=225
Right here

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