Answer
$z=\frac {i\sqrt 2}{2}, \frac {-i\sqrt 2}{2}, \frac {i\sqrt {5}}{2}, \frac {-i\sqrt {5}}{2}$
Work Step by Step
$8z^4+14z^2=-5$
$z^2=x$
$8z^4+14z^2=-5$
$8(z^2)^2+14z^2=-5$
$8x^2+14x+5=0$
$x=(-b±\sqrt {b^2-4ac})/2a$
$x=(-14±\sqrt {14^2-4*8*5})/2*8$
$x=(-14±\sqrt {196-32*5})/16$
$x=(-14±\sqrt {196-160})/16$
$x=(-14±\sqrt {36})/16$
$x=(-14±6)/16$
$x=(-14±6)/16$
$x=(-14+6)/16$
$x=(-8/16)$
$x=-1/2$
$x=(-14±6)/16$
$x=(-14-6)/16$
$x=-20/16$
$x=-5/4$
$x=-1/2$
$x=-5/4$
$z^2=x$
$z^2=-1/2$
$\sqrt {z^2}=\sqrt {-1/2}$
$z=\sqrt {-1*1/2}$
$z=\frac {\sqrt {-1*1}}{\sqrt 2}$
$z=\frac {i\sqrt {1}}{\sqrt 2}$
$z=\frac {±i}{\sqrt 2}$
$z=\frac {±i*\sqrt 2}{\sqrt 2*\sqrt 2}$
$z=\frac {±i*\sqrt 2}{2}$
$z^2=-5/4$
$\sqrt {z^2}=\sqrt {-5/4}$
$z=\sqrt {-1*5/4}$
$z=\frac {\sqrt {-1*5}}{\sqrt 4}$
$z=\frac {±i\sqrt {5}}{\sqrt 4}$
$z=\frac {±i\sqrt {5}}{2}$
