SOLUTION: A photograph has a length that is 2 inches longer than its width, x. So its area is given by the expression x(x+2) square inches. If the area of the photograph is 48 square inches,

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: A photograph has a length that is 2 inches longer than its width, x. So its area is given by the expression x(x+2) square inches. If the area of the photograph is 48 square inches,      Log On


   

Question 954418: A photograph has a length that is 2 inches longer than its width, x. So its area is given by the expression x(x+2) square inches. If the area of the photograph is 48 square inches, what is the width of the photograph
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
x%28x%2B2%29=48
x%5E2%2B2x=48
(((x^2+2x-48=0}}}
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B2x%2B-48+=+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-48=196.

Discriminant d=196 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-2%2B-sqrt%28+196+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%282%29%2Bsqrt%28+196+%29%29%2F2%5C1+=+6
x%5B2%5D+=+%28-%282%29-sqrt%28+196+%29%29%2F2%5C1+=+-8

Quadratic expression 1x%5E2%2B2x%2B-48 can be factored:
1x%5E2%2B2x%2B-48+=+1%28x-6%29%2A%28x--8%29
Again, the answer is: 6, -8. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B2%2Ax%2B-48+%29

ANSWER: The width is 6 inches.
CHECK:
Length=Width+2=6 in + 2 in=8 in
Area=L*W
48 sq in=8 in*6 in
48 sq in=48 sq in