SOLUTION: The length of this rectangle is 1cm more than its width.It has an area of 232cm2.Find the width of the rectangle correct to 1 d.p.

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Question 283090: The length of this rectangle is 1cm more than its width.It has an area of 232cm2.Find the width of the rectangle correct to 1 d.p.
Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
x*(x+1)=232
x^2+x-232=0
we only use the positive root 14.7 for the width
length would be 14.7+1
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B1x%2B-232+=+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=%281%29%5E2-4%2A1%2A-232=929.

Discriminant d=929 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-1%2B-sqrt%28+929+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%281%29%2Bsqrt%28+929+%29%29%2F2%5C1+=+14.7397506541282
x%5B2%5D+=+%28-%281%29-sqrt%28+929+%29%29%2F2%5C1+=+-15.7397506541282

Quadratic expression 1x%5E2%2B1x%2B-232 can be factored:
1x%5E2%2B1x%2B-232+=+1%28x-14.7397506541282%29%2A%28x--15.7397506541282%29
Again, the answer is: 14.7397506541282, -15.7397506541282. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B1%2Ax%2B-232+%29