SOLUTION: i'm learning polynomials and such in class and a question came up in one of my group tests. i asked someone else for help and they showed me how to do it but i don't get how to get

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Question 385217: i'm learning polynomials and such in class and a question came up in one of my group tests. i asked someone else for help and they showed me how to do it but i don't get how to get from the equation to the answer.
i do not understand how 2w^2+11w=84 gets to whatever the weird answer was. i do not understand how it is a quadratic equation and how to simplify it...please help and thanks so much.
PS. the problem i had on my group test was this:
The length of a picture is one inch less than twice its width. the frame around the picture has a uniform width of two inches and an area of 96 square inches. what are the dimensions of the picture?
i did the equation like this:
(2w+3)(w+4)=96
which simplified to:
2w^2+11w=84
Found 2 solutions by stanbon, mananth:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
i do not understand how 2w^2+11w=84 gets to whatever the weird answer was. i do not understand how it is a quadratic equation and how to simplify it...please help and thanks so much.
PS. the problem i had on my group test was this:
The length of a picture is one inch less than twice its width. the frame around the picture has a uniform width of two inches and an area of 96 square inches. what are the dimensions of the picture?
i did the equation like this:
(2w+3)(w+4)=96
which simplified to:
2w^2+11w=84
----
It's the frame that has an area of 96 sq. inches, not the entire picture.
----
Cheers,
Stan H.

Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
The length of a picture is one inch less than twice its width. the frame around the picture has a uniform width of two inches and an area of 96 square inches. what are the dimensions of the picture?
...
width of picture = w
length = 2w-1
...
Area of picture = w(2w-1)
...
uniform width of 2 in.surrounding the picture
so width will be w+4
length = (2w-1)+4=2w+3
..
Area of picture + area frame =(w+4)(2w+3)
...
(Area of picture + area frame)-area of picture= area of frame
..
(w+3)(2w+3)-w(2w-1)=96
2w^2+9w+9-2w^2+w=96
10w+9=96
-9 -9
10w=87
/10
%28highlight%28w=8.7%29%29cm the width
Length = 2w-1= 2*8.7-1
Length =17.4-1
Length%28highlight%28l=16.4%29%29cm