SOLUTION: z ( Z-9) = -2

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Question 237535: z ( Z-9) = -2
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
z ( z-9) = -2
z^2-9z=-2
z^2-9z+2=0
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Ed
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Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-9x%2B2+=+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=%28-9%29%5E2-4%2A1%2A2=73.

Discriminant d=73 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--9%2B-sqrt%28+73+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-9%29%2Bsqrt%28+73+%29%29%2F2%5C1+=+8.77200187265877
x%5B2%5D+=+%28-%28-9%29-sqrt%28+73+%29%29%2F2%5C1+=+0.227998127341235

Quadratic expression 1x%5E2%2B-9x%2B2 can be factored:
1x%5E2%2B-9x%2B2+=+1%28x-8.77200187265877%29%2A%28x-0.227998127341235%29
Again, the answer is: 8.77200187265877, 0.227998127341235. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-9%2Ax%2B2+%29