SOLUTION: x/(5x-25) - 2 = x/(1-5) simplify and solve for x

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Question 344719: x/(5x-25) - 2 = x/(1-5) simplify and solve for x
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
x%2F%285x-25%29+-+2+=+x%2F%281-5%29
Simplify:
x%2F%285x-25%29+-+2+=+-x%2F4
4x%2F%285x-25%29+-+8+=+-x
4x-+8%285x-25%29+=+-x%285x-25%29
4x- 40x + 200 = -5x^(2)+25x
5x^2 - 61x + 200 = 0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 5x%5E2%2B-61x%2B200+=+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=%28-61%29%5E2-4%2A5%2A200=-279.

The discriminant -279 is less than zero. That means that there are no solutions among real numbers.

If you are a student of advanced school algebra and are aware about imaginary numbers, read on.


In the field of imaginary numbers, the square root of -279 is + or - sqrt%28+279%29+=+16.7032930884901.

The solution is

Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+5%2Ax%5E2%2B-61%2Ax%2B200+%29