SOLUTION: solve: you have made a quilt that is 4ft by 5 ft. you want to use the remaining 10 square feet of fabric to add a decorative border of uniform width. what should the width of the

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: solve: you have made a quilt that is 4ft by 5 ft. you want to use the remaining 10 square feet of fabric to add a decorative border of uniform width. what should the width of the       Log On


   

Question 278634: solve: you have made a quilt that is 4ft by 5 ft. you want to use the remaining 10 square feet of fabric to add a decorative border of uniform width. what should the width of the border be?
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
4*5=20 ft^2
(4+x)+(5+x)=30 ft^2
20+9x+x^2=30
x^2+9x-10=0
(x+10)*(x-1)=0
x=1
check
5*6=30
ok
add one foot border to each side.
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B9x%2B-10+=+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=%289%29%5E2-4%2A1%2A-10=121.

Discriminant d=121 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-9%2B-sqrt%28+121+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%289%29%2Bsqrt%28+121+%29%29%2F2%5C1+=+1
x%5B2%5D+=+%28-%289%29-sqrt%28+121+%29%29%2F2%5C1+=+-10

Quadratic expression 1x%5E2%2B9x%2B-10 can be factored:
1x%5E2%2B9x%2B-10+=+1%28x-1%29%2A%28x--10%29
Again, the answer is: 1, -10. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B9%2Ax%2B-10+%29