SOLUTION: Help! Don't know how to put story problem into quadratic formula: A rectangular garden is 30 ft by 40 ft. Part of the garden is removed in order to install a walkway of uniform

Question 833912: Help! Don't know how to put story problem into quadratic formula:
A rectangular garden is 30 ft by 40 ft. Part of the garden is removed in order to install a walkway of uniform width around it. The area of the new garden is one-half the area of the old garden. How wide is the walkway?
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
A rectangular garden is 30 ft by 40 ft. Part of the garden is removed in order to install a walkway of uniform width around it. The area of the new garden is one-half the area of the old garden. How wide is the walkway?

Area of the entire garden is
Let be the width of the walkway.
Length of the reduced garden is
Width of the reduced garden is
Area of the reduced garden is

Area of the reduced garden is one-half the area of the old garden; so, we have
or

since
and , we have

...simplify
....expand

...both sides divide by
......solve for

Solved by pluggable solver: Quadratic Formula

Let's use the quadratic formula to solve for x:

Starting with the general quadratic

the general solution using the quadratic equation is:

So lets solve ( notice , , and )

Plug in a=4, b=-140, and c=600

Negate -140 to get 140

Square -140 to get 19600 (note: remember when you square -140, you must square the negative as well. This is because .)

Multiply to get

Combine like terms in the radicand (everything under the square root)

Simplify the square root (note: If you need help with simplifying the square root, check out this solver)

Multiply 2 and 4 to get 8

So now the expression breaks down into two parts

or

Lets look at the first part:

Add the terms in the numerator

Divide

So one answer is

Now lets look at the second part:

Subtract the terms in the numerator

Divide

So another answer is

So our solutions are:

or

If , the length is
and width
If , the length is
and width
So, the second case () is ruled out because you can't have a width and a length equal to negative number.

so the walkway is wide

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