Question 1128874


{{{f(x)=(1/4)x^2}}}

{{{g(x)=-1+(1/3)x}}}

find: {{{f(x)=g(x)}}}


{{{(1/4)x^2=-1+(1/3)x}}}


{{{(1/4)x^2+1-(1/3)x=0}}}....each term multiply by {{{12}}}


{{{12(1/4)x^2+1*12-12(1/3)x=0}}}


{{{cross(12)3(1/cross(4))x^2-cross(12)4(1/cross(3))x+12=0}}}


{{{3x^2-4x+12=0}}}...use quadratic formula


{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} ..in your case, {{{a=3}}}, {{{b=-4}}}, and {{{c=12}}}


{{{x = (-(-4) +- sqrt( (-4)^2-4*3*12 ))/(2*3) }}} 


{{{x = (4 +- sqrt( 16-144 ))/6 }}} 


{{{x = (4 +- sqrt( -128 ))/6 }}} 


{{{x = (4 +- sqrt( -1*2*64 ))/6 }}} 


{{{x = (4 +- 8sqrt(2)*i)/6 }}} ...simplify


{{{x = (2 +- 4sqrt(2)*i)/3 }}} 


{{{x = (2/3 +- 4sqrt(2)*i/3) }}} 



solutions:

{{{x = (2 + 4sqrt(2)*i)/3 }}} =>{{{x = 2/3 + 4sqrt(2)*i/3 }}} 


{{{x = (2 - 4sqrt(2)*i)/3 }}} =>{{{x = 2/3- 4sqrt(2)*i/3 }}}