SOLUTION: solve for x. show all work. 2-4/x^2=-2/x

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Question 939030: solve for x. show all work.
2-4/x^2=-2/x
Answer by srinivas.g(540) About Me  (Show Source):
You can put this solution on YOUR website!
2-4%2Fx%5E2=-2%2Fx
Multiply each term with x%5E2
+2%2Ax%5E2-%284%2Fx%5E2%29%2Ax%5E2=%28-2%2Fx%29%2Ax%5E2
2x%5E2-4=-2x
Move-2x to the left
2x%5E2-4%2B2x=0
2x%5E2%2B2x-4=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B2x%2B-4+=+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=%282%29%5E2-4%2A2%2A-4=36.

Discriminant d=36 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-2%2B-sqrt%28+36+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%282%29%2Bsqrt%28+36+%29%29%2F2%5C2+=+1
x%5B2%5D+=+%28-%282%29-sqrt%28+36+%29%29%2F2%5C2+=+-2

Quadratic expression 2x%5E2%2B2x%2B-4 can be factored:
2x%5E2%2B2x%2B-4+=+2%28x-1%29%2A%28x--2%29
Again, the answer is: 1, -2. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B2%2Ax%2B-4+%29