SOLUTION: what is the value of x -2x^2+6x=-3

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Question 896096: what is the value of x
-2x^2+6x=-3
Answer by TheInstructor(29) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -2x%5E2%2B6x%2B3+=+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=%286%29%5E2-4%2A-2%2A3=60.

Discriminant d=60 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-6%2B-sqrt%28+60+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%286%29%2Bsqrt%28+60+%29%29%2F2%5C-2+=+-0.436491673103709
x%5B2%5D+=+%28-%286%29-sqrt%28+60+%29%29%2F2%5C-2+=+3.43649167310371

Quadratic expression -2x%5E2%2B6x%2B3 can be factored:
-2x%5E2%2B6x%2B3+=+-2%28x--0.436491673103709%29%2A%28x-3.43649167310371%29
Again, the answer is: -0.436491673103709, 3.43649167310371. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-2%2Ax%5E2%2B6%2Ax%2B3+%29