SOLUTION: I need help with a quadratic word problem. Picture framing: the matting around the picture has a uniform width. How wide is the matting if its area equals the area of the pictu

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: I need help with a quadratic word problem. Picture framing: the matting around the picture has a uniform width. How wide is the matting if its area equals the area of the pictu      Log On


   

Question 876709: I need help with a quadratic word problem.
Picture framing: the matting around the picture has a uniform width. How wide is the matting if its area equals the area of the picture? round to the nearest hundredth of an inch. The picture is 5inches by 4 inches, thanks

Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = the width of the matting.
The area of the picture = area of matting = 5*4 = 20
(2x+5)(2x+4)= 40 in^2
4x^2+18x+20=40
4x^2+18x-20=0
x=0.92"
.
Ed
.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 4x%5E2%2B18x%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=%2818%29%5E2-4%2A4%2A-20=644.

Discriminant d=644 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-18%2B-sqrt%28+644+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2818%29%2Bsqrt%28+644+%29%29%2F2%5C4+=+0.92214438511238
x%5B2%5D+=+%28-%2818%29-sqrt%28+644+%29%29%2F2%5C4+=+-5.42214438511238

Quadratic expression 4x%5E2%2B18x%2B-20 can be factored:
4x%5E2%2B18x%2B-20+=+4%28x-0.92214438511238%29%2A%28x--5.42214438511238%29
Again, the answer is: 0.92214438511238, -5.42214438511238. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B18%2Ax%2B-20+%29