Question 652630
{{{10(x^(-2))+33x^(-1)-7=0 }}}


{{{(10/x^2)+(33/x)-7=0 }}}....find common denominator


{{{(10x+33x^2-7x^3)/x^3=0 }}}


{{{10x+33x^2-7x^3=0*x^3 }}}


{{{-7x^3+33x^2+10x=0 }}}...factor


{{{x(-7x^2+33x+10)=0 }}}... replace {{{33x}}} with {{{35x-2x}}}


{{{x(-7x^2+35x-2x+10)=0 }}}...group


{{{x((-7x^2+35x)-(2x-10))=0 }}}


{{{x(-7x(x-5)-2(x-5))=0 }}}


{{{x(-7x-2)(x-5))=0 }}}


{{{x*-1(7x+2)(x-5))=0 }}}


{{{-x(7x+2)(x-5))=0 }}}


solutions:


if {{{-x=0 }}} ....->...{{{x=0}}}


if {{{7x+2=0 }}}....->...{{{7x=-2 }}}..->...{{{x=-2/7 }}}


if {{{x-5=0 }}}...->...{{{x=5}}}



{{{ graph( 600, 600, -5, 7, -5, 30, -x*(7x+2)*(x-5)) }}}