SOLUTION: The length of the top of a table is 7m greater than the width. the area is 78m^2. find the dimensions of the table

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Question 446089: The length of the top of a table is 7m greater than the width.
the area is 78m^2. find the dimensions of the table
Answer by chriswen(106) About Me  (Show Source):
You can put this solution on YOUR website!
Let x be the width.
Let x+7 be the length.
...
l*w=A
%28x%29%28x%2B7%29=78
x%5E2%2B7x=78
x%5E2%2B7x-78=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B7x%2B-78+=+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=%287%29%5E2-4%2A1%2A-78=361.

Discriminant d=361 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-7%2B-sqrt%28+361+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%287%29%2Bsqrt%28+361+%29%29%2F2%5C1+=+6
x%5B2%5D+=+%28-%287%29-sqrt%28+361+%29%29%2F2%5C1+=+-13

Quadratic expression 1x%5E2%2B7x%2B-78 can be factored:
1x%5E2%2B7x%2B-78+=+1%28x-6%29%2A%28x--13%29
Again, the answer is: 6, -13. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B7%2Ax%2B-78+%29

There are two answers 6 and -13. Since, we are dealing with positive numbers x must x= 6.
And x+7=13
So therefore, the dimensions of the rectangle is 6 by 13.