SOLUTION: the area of the rectangle is 15cm^. find the value of x. height is x and the base is x+3

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Question 827232: the area of the rectangle is 15cm^. find the value of x.
height is x and the base is x+3

Found 2 solutions by LinnW, josgarithmetic:
Answer by LinnW(1048) About Me  (Show Source):
You can put this solution on YOUR website!
area = length x width
15 = (x)(x+3)
15 = x^2 + 3x
subtract 15 from each side.
0 = x^2 + 3x -15
x^2 + 3x -15 = 0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B3x%2B-15+=+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=%283%29%5E2-4%2A1%2A-15=69.

Discriminant d=69 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-3%2B-sqrt%28+69+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%283%29%2Bsqrt%28+69+%29%29%2F2%5C1+=+2.65331193145904
x%5B2%5D+=+%28-%283%29-sqrt%28+69+%29%29%2F2%5C1+=+-5.65331193145904

Quadratic expression 1x%5E2%2B3x%2B-15 can be factored:
1x%5E2%2B3x%2B-15+=+1%28x-2.65331193145904%29%2A%28x--5.65331193145904%29
Again, the answer is: 2.65331193145904, -5.65331193145904. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B3%2Ax%2B-15+%29


The value of the other dimension x+3 = 2.65+3 = 5.65

Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Area=(base)(height)
x%28x%2B3%29=15
'
x%5E2%2B3x=15
x%5E2%2B3x-15=0, not factorable
'
x=%28-3%2Bsqrt%289%2B4%2A15%29%29%2F%282%29