SOLUTION: I am trying to work the following problem, but am unsure how to go about doing so. Find all values of x if f(x)=-38: f(x)=5x+21/x This is what I have gotten so far: f(x

Algebra ->  Rational-functions -> SOLUTION: I am trying to work the following problem, but am unsure how to go about doing so. Find all values of x if f(x)=-38: f(x)=5x+21/x This is what I have gotten so far: f(x      Log On


   

Question 145362: I am trying to work the following problem, but am unsure how to go about doing so.
Find all values of x if f(x)=-38:
f(x)=5x+21/x
This is what I have gotten so far:
f(x)=5(-38)+[21/(-38)]
f(x)=-190+(21/-38)
What do I do from here?
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
Find all values of x if f(x)=-38:
f(x)=5x+21/x
-38 = 5x + 21/x
-38x = 5x^2 + 21
0 = 5x^2 + 38x + 21
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 5x%5E2%2B38x%2B21+=+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=%2838%29%5E2-4%2A5%2A21=1024.

Discriminant d=1024 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-38%2B-sqrt%28+1024+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2838%29%2Bsqrt%28+1024+%29%29%2F2%5C5+=+-0.6
x%5B2%5D+=+%28-%2838%29-sqrt%28+1024+%29%29%2F2%5C5+=+-7

Quadratic expression 5x%5E2%2B38x%2B21 can be factored:
5x%5E2%2B38x%2B21+=+5%28x--0.6%29%2A%28x--7%29
Again, the answer is: -0.6, -7. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+5%2Ax%5E2%2B38%2Ax%2B21+%29