SOLUTION: 2(x-3)^(2)=-2x+9

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Question 583178: 2(x-3)^(2)=-2x+9
Answer by tommyt3rd(5050) About Me  (Show Source):
You can put this solution on YOUR website!
if you mean solve, then...
2(x-3)^(2)=-2x+9
2(x^2-6x+9)=-2x+9
2x^2-10x+9=0

Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B-10x%2B9+=+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=%28-10%29%5E2-4%2A2%2A9=28.

Discriminant d=28 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--10%2B-sqrt%28+28+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-10%29%2Bsqrt%28+28+%29%29%2F2%5C2+=+3.8228756555323
x%5B2%5D+=+%28-%28-10%29-sqrt%28+28+%29%29%2F2%5C2+=+1.1771243444677

Quadratic expression 2x%5E2%2B-10x%2B9 can be factored:
2x%5E2%2B-10x%2B9+=+2%28x-3.8228756555323%29%2A%28x-1.1771243444677%29
Again, the answer is: 3.8228756555323, 1.1771243444677. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B-10%2Ax%2B9+%29