Question 481235


{{{25x-50=-23/x}}}..to solve for {{{x}}}, firs both sides multiply by denominator {{x}}}

{{{25x*x-50*x=-23*x/x}}}


{{{25x^2-50x=-23*cross(x)/cross(x)}}}


{{{25x^2-50x=-23}}}.......move {{{-23}}} to the left side

{{{25x^2-50x+23=0}}}....use quadratic formula to solve for {{{x}}}


{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}...note {{{a=25}}}, {{{b=-50}}} and {{{c=23}}}


{{{x = (-(-50) +- sqrt( (-50)^2-4*25*23 ))/(2*25) }}}


{{{x = (50+- sqrt(2500-2300 ))/50 }}}


{{{x = (50+- sqrt(200 ))/50 }}}


{{{x = (50+- 14.14)/50 }}}


solutions:

{{{x = (50+ 14.14)/50 }}}


{{{x = (64.14)/50 }}}


{{{highlight(x = 1.2828) }}}

or

{{{x = (50-14.14)/50 }}}


{{{x = (35.86)/50 }}}


{{{highlight(x = 0.7172) }}}