Answer
$x=-.5, .5, -i\sqrt 3, i\sqrt 3$
Work Step by Step
$4x^4+11x^2=3$
$y=x^2$
$4x^4+11x^2=3$
$4(x^2)^2+11x^2-3=3-3$
$4y^2+11y-3=0$
$y=(-b±\sqrt {b^2-4ac})/2a$
$y=(-11±\sqrt {11^2-4*4*-3})/2*4$
$y=(-11±\sqrt {121+48})/8$
$y=(-11±\sqrt {169})/8$
$y=(-11±13)/8$
$y=(-11+13)/8$
$y=2/8$
$y=1/4$
$y=(-11-13)/8$
$y=-24/8$
$y=-3$
$y=x^2$
$1/4=x^2$
$\sqrt {1/4} =\sqrt {x^2}$
$x=±1/2$
$x^2=-3$
$\sqrt {x^2} = \sqrt {-3}$
$x=\sqrt {-3}$
$x=\sqrt {3*-1}$
$x=±i\sqrt3$
