SOLUTION: 1/x^2 + 8/x= -2

Algebra ->  Test  -> Lessons -> SOLUTION: 1/x^2 + 8/x= -2      Log On


   

Question 472114: 1/x^2 + 8/x= -2
Answer by jorel1380(3719) About Me  (Show Source):
You can put this solution on YOUR website!
1/x^2 + 8/x= -2
1+8x=-2x2
2x2+8x+1=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 2x%5E2%2B8x%2B1+=+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=%288%29%5E2-4%2A2%2A1=56.

Discriminant d=56 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-8%2B-sqrt%28+56+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%288%29%2Bsqrt%28+56+%29%29%2F2%5C2+=+-0.129171306613029
x%5B2%5D+=+%28-%288%29-sqrt%28+56+%29%29%2F2%5C2+=+-3.87082869338697

Quadratic expression 2x%5E2%2B8x%2B1 can be factored:
2x%5E2%2B8x%2B1+=+2%28x--0.129171306613029%29%2A%28x--3.87082869338697%29
Again, the answer is: -0.129171306613029, -3.87082869338697. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B8%2Ax%2B1+%29