SOLUTION: 50- x^2 / 2

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Question 595373: 50- x^2 / 2
Answer by math33(31) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 4x%5E2%2B6x%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=%286%29%5E2-4%2A4%2A2=4.

Discriminant d=4 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-6%2B-sqrt%28+4+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%286%29%2Bsqrt%28+4+%29%29%2F2%5C4+=+-0.5
x%5B2%5D+=+%28-%286%29-sqrt%28+4+%29%29%2F2%5C4+=+-1

Quadratic expression 4x%5E2%2B6x%2B2 can be factored:
4x%5E2%2B6x%2B2+=+%28x--0.5%29%2A%28x--1%29
Again, the answer is: -0.5, -1. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B6%2Ax%2B2+%29