SOLUTION: Please help w/ the following: 2x^-2+3x^-1+1=0 Thank you.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Please help w/ the following: 2x^-2+3x^-1+1=0 Thank you.      Log On


   

Question 59097: Please help w/ the following:
2x^-2+3x^-1+1=0
Thank you.
Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
2x%5E%28-2%29%2B3x%5E%28-1%29%2B1=0
2%28x%5E%28-1%29%29%5E2%2B3%28x%5E%28-1%29%29%2B1=0
Let x%5E%28-1%29=p
2p%5E2%2B3p%2B1=0
(2p+1)(p+1)=0
2p+1=0 and p+1=0
2p+1-1=0-1 and p+1-1=0-1
2p=-1 and p=-1
2p/2=-1/2 and p=-1
p=-1/2 and p=-1
But we want to know what x is so let p=x%5E%28-1%29
x%5E%28-1%29=-1%2F2 and x%5E%28-1%29=-1
%28x%5E%28-1%29%29%5E%28-1%29=%28-1%2F2%29%5E%28-1%29 and %28x%5E%28-1%29%29%5E%28-1%29=%28-1%29%5E%28-1%29
highlight%28x=-2%29 and highlight%28x=-1%29
:
Check:
2%28-2%29%5E%28-2%29%2B3%28-2%29%5E%28-1%29%2B1=0
2%281%2F4%29%2B3%28-1%2F2%29%2B1=0
1%2F2-3%2F2%2B1=0
-2%2F2%2B1=0
-1%2B1=0
0=0 x=-2 checks out.
:
2%28-1%29%5E%28-2%29%2B3%28-1%29%5E%28-1%29%2B1=0
2%281%29%2B3%28-1%29%2B1=0
2-3%2B1=0
0=0 x=-1 checks out too.
Happy Calculating!!!