SOLUTION: Solve fir r: r with the exponent of 2 + 5r - 14 = 0

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Question 96559: Solve fir r: r with the exponent of 2 + 5r - 14 = 0

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ar%5E2%2Bbr%2Bc=0 (in our case 1r%5E2%2B5r%2B-14+=+0) has the following solutons:

r%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=%285%29%5E2-4%2A1%2A-14=81.

Discriminant d=81 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-5%2B-sqrt%28+81+%29%29%2F2%5Ca.

r%5B1%5D+=+%28-%285%29%2Bsqrt%28+81+%29%29%2F2%5C1+=+2
r%5B2%5D+=+%28-%285%29-sqrt%28+81+%29%29%2F2%5C1+=+-7

Quadratic expression 1r%5E2%2B5r%2B-14 can be factored:
1r%5E2%2B5r%2B-14+=+1%28r-2%29%2A%28r--7%29
Again, the answer is: 2, -7. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B5%2Ax%2B-14+%29