Question 1156555

{{{f(x) = x^2(2e^(6x)) + 4xe^(6x) + 7e^(6x) + 4xe^(6x)}}}

{{{f(x) =0}}}

 {{{2x^2*e^(6x) + 4xe^(6x) + 7e^(6x) + 4xe^(6x)=0}}}

{{{(2x^2 + 4x + 7 + 4x)e^(6x)=0}}}

{{{(2x^2 + 8x + 7 )e^(6x)=0}}}

{{{e^(6x)=0 }}}=>no solutions exist 

{{{2x^2 + 8x + 7 =0}}}......use quadratic formula

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

{{{x=(-8+-sqrt(8^2-4*2*7))/(2*2)}}}

{{{x=(-8+-sqrt(64-56))/4}}}

{{{x=(-8+-sqrt(8))/4}}}

{{{x=(-8+-sqrt(4*2))/4}}}

{{{x=(-8+-2sqrt(2))/4}}}

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

solutions:

{{{x=(-4+sqrt(2))/2}}}
{{{x=-2+sqrt(2)/2}}}...rationalize:  {{{sqrt(2)/2=(sqrt(2)*sqrt(2))/2sqrt(2)=2/2sqrt(2)=1/sqrt(2)}}}

{{{highlight(x = -2 + 1/sqrt(2))}}}


{{{x=(-4-sqrt(2))/2}}}...rationalize, same as above 

{{{highlight(x=-2-1/sqrt(2))}}}