Question 32364
First, always try and solve by factoring.  This one happens to be factorable.
{{{ x^4 -5x^2 - 36=0 }}}
-9 * 4 = 36 and -9 + 4 = -5
{{{ (x^2 -9)(x^2 + 4) =0 }}}
Continue factoring
{{{ (x-3)(x+3)(x^2+4)=0 }}}
Set each piece equal to zero
{{{ x-3=0 }}} and {{{ x+3 = 0 }}} and {{{ x^2+4=0 }}}
{{{ x=3 }}} and {{{ x=-3 }}} and {{{ x^2 = -4 }}}
{{{ x=3 }}} and {{{ x=-3 }}} and {{{ sqrt(x^2) = sqrt(-4) }}}
{{{ x=3 }}} and {{{ x=-3 }}} and {{{ x = sqrt(-4) }}}
{{{ x=3 }}} and {{{ x=-3 }}} and {{{ x = i(sqrt(4)) }}}
{{{ x=3 }}} and {{{ x=-3 }}} and {{{ x = 2i }}}
assuming your instructor wants ONLY real roots, then x = {3, -3 }
If s/he wants all roots ... x = { -3, 3, 2i }