SOLUTION: The length of rectangular mural is 2m greater than the width. The area is 20m squared. Find the dimensions of the mural.

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Question 132661: The length of rectangular mural is 2m greater than the width. The area is 20m squared. Find the dimensions of the mural.
Answer by snwbrdfrk(10) About Me  (Show Source):
You can put this solution on YOUR website!
since you know the total area is 20 and you know that one side of the mural is 2m longer you need to set an equation up
x = first side
x+2 = side 2m longer
20 = total area
x(x+2)=20
x^2 + 2x = 20
x^2 + 2x - 20 = 0
youll need to use the quadratic equation for this

Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B2x%2B-20+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%282%29%5E2-4%2A1%2A-20=84.

Discriminant d=84 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-2%2B-sqrt%28+84+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%282%29%2Bsqrt%28+84+%29%29%2F2%5C1+=+3.58257569495584
x%5B2%5D+=+%28-%282%29-sqrt%28+84+%29%29%2F2%5C1+=+-5.58257569495584

Quadratic expression 1x%5E2%2B2x%2B-20 can be factored:
1x%5E2%2B2x%2B-20+=+%28x-3.58257569495584%29%2A%28x--5.58257569495584%29
Again, the answer is: 3.58257569495584, -5.58257569495584. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B2%2Ax%2B-20+%29


dont worry about the graph if you see it
you will get two answers and since you are dealing with lengths the answer that was negative wont work making 3.582 your answer for x
x = 3.582
x+2 = 5.582