Question 177076
You can't <i><b>solve</b></i> {{{x^4+5x^2+9}}}, because you haven't set your expression equal to anything.  Now if what you meant was {{{x^4+5x^2+9 = 0}}}, THEN you have something that you can solve.


Let {{{t = x^2}}}, then {{{x^4 + 5x^2 + 9 = 0}}} is equivalent to {{{t^2 + 5t + 9 = 0}}}, which is a quadratic that needs to be solved with the quadratic formula:


{{{t = (-5 +- sqrt( 25-36 ))/2 = (-5 +- i*sqrt(11))/2 }}}


but {{{t = x^2}}} so:


{{{x[1] = sqrt( (-5 + i*sqrt(11))/2 ) = i*sqrt(5)/2 + sqrt(i*sqrt(11))/2)}}} or 


{{{x[2] = -sqrt( (-5 + i*sqrt(11))/2 ) = -i*sqrt(5)/2 - sqrt(i*sqrt(11))/2)}}} or


{{{x[3] = sqrt( (-5 - i*sqrt(11))/2 ) = i*sqrt(5)/2 - sqrt(i*sqrt(11))/2)}}} or 


{{{x[4] = -sqrt( (-5 - i*sqrt(11))/2 ) = -i*sqrt(5)/2 + sqrt(i*sqrt(11))/2)}}}