SOLUTION: solve for r r^2+3r=6 type an exact answer using radicals as needed

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Question 353839: solve for r
r^2+3r=6
type an exact answer using radicals as needed
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
solve for r
r^2+3r=6
r%5E2+%2B+3r+-+6+=+0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B3x%2B-6+=+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-6=33.

Discriminant d=33 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-3%2B-sqrt%28+33+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%283%29%2Bsqrt%28+33+%29%29%2F2%5C1+=+1.37228132326901
x%5B2%5D+=+%28-%283%29-sqrt%28+33+%29%29%2F2%5C1+=+-4.37228132326901

Quadratic expression 1x%5E2%2B3x%2B-6 can be factored:
1x%5E2%2B3x%2B-6+=+%28x-1.37228132326901%29%2A%28x--4.37228132326901%29
Again, the answer is: 1.37228132326901, -4.37228132326901. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B3%2Ax%2B-6+%29

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r = x
r+=+%28-3%2F2%29+%2B+sqrt%2833%29%2F2
r+=+%28-3%2F2%29+-+sqrt%2833%29%2F2