Question 996297

{{{x^3-5x^2-x=0 }}}

{{{x(x^2-5x-1)=0 }}}

one solution is {{{highlight(x=0)}}}

now use quadratic formula to find other two solutions

{{{(x^2-5x-1)=0 }}}

{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}

{{{x = (-(-5) +- sqrt( (-5)^2-4*1*(-1) ))/(2*1) }}}


{{{x = (5 +- sqrt( 25+4 ))/2 }}}


{{{x = (5 +- sqrt( 29 ))/2 }}}

exact solutions:

{{{highlight(x = (5 + sqrt( 29 ))/2) }}}

{{{highlight(x = (5 - sqrt( 29 ))/2 )}}}

approximate solutions:

{{{x = (5 + sqrt( 29 ))/2 }}}=>{{{x = (5 + 5.4)/2 }}}=>{{{x = 10.4/2 }}}=>{{{highlight(x = 5.2) }}}

{{{x = (5 - sqrt( 29 ))/2 }}}=>{{{x = (5 - 5.4)/2 }}}=>{{{x = -0.4/2 }}}=>{{{highlight(x = -0.2 )}}}