Question 59097
{{{2x^(-2)+3x^(-1)+1=0}}}
{{{2(x^(-1))^2+3(x^(-1))+1=0}}}
Let {{{x^(-1)=p}}}
{{{2p^2+3p+1=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^(-1)}}}
{{{x^(-1)=-1/2}}} and {{{x^(-1)=-1}}}
{{{(x^(-1))^(-1)=(-1/2)^(-1)}}} and {{{(x^(-1))^(-1)=(-1)^(-1)}}}
{{{highlight(x=-2)}}} and {{{highlight(x=-1)}}}
:
Check:
{{{2(-2)^(-2)+3(-2)^(-1)+1=0}}}
{{{2(1/4)+3(-1/2)+1=0}}}
{{{1/2-3/2+1=0}}}
{{{-2/2+1=0}}}
{{{-1+1=0}}}
{{{0=0}}}  x=-2 checks out.
:
{{{2(-1)^(-2)+3(-1)^(-1)+1=0}}}
{{{2(1)+3(-1)+1=0}}}
{{{2-3+1=0}}}
{{{0=0}}}  x=-1  checks out too.
Happy Calculating!!!