SOLUTION: 1/4 = 3 - 2x -1/x + 2

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Question 146791: 1/4 = 3 - 2x -1/x + 2
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
1/4 = 3 - 2x - 1/x + 2
x=12x-8x^2-4+8x Multiply each side by 4x (LCM) to eliminate fractions.
-8x^2+12x-x+8x-4=0
-8x^2+19x-4=0
8x^2-19x+4=0
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Ed
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Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 8x%5E2%2B-19x%2B4+=+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=%28-19%29%5E2-4%2A8%2A4=233.

Discriminant d=233 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--19%2B-sqrt%28+233+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-19%29%2Bsqrt%28+233+%29%29%2F2%5C8+=+2.14152109515461
x%5B2%5D+=+%28-%28-19%29-sqrt%28+233+%29%29%2F2%5C8+=+0.233478904845391

Quadratic expression 8x%5E2%2B-19x%2B4 can be factored:
8x%5E2%2B-19x%2B4+=+%28x-2.14152109515461%29%2A%28x-0.233478904845391%29
Again, the answer is: 2.14152109515461, 0.233478904845391. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+8%2Ax%5E2%2B-19%2Ax%2B4+%29