Question 1020787
Make the substitution:
{{{ z = x^2 }}}
{{{ x^4 + 11x^2 + 18 = 0 }}}
{{{ z^2 + 11z + 18 = 0 }}}
By looking at this:
{{{ ( z + 9 )*( z + 2 ) = 0 }}}
{{{ z = -9 }}}
{{{ z = -2 }}}
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Plug these results back into substitution
{{{ z = x^2 }}}
{{{ -2 = x^2 }}}
{{{ x = sqrt(2)*i }}}
and, also:
{{{ x = -sqrt(2)*i }}}
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{{{ -9 = x^2 }}}
{{{ x = 3i }}}
{{{ x = -3i }}}
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The roots are:
{{{ sqrt(2)*i }}}  , {{{ -sqrt(2)*i }}} , {{{ 3i }}} , {{{ -3i }}} 
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 check answer:
{{{ ( x + sqrt(2)*i )*( x - sqrt(2)*i )*( x - 3i )*( x + 3i ) = 0 }}}
{{{ ( x^2 + 2 )*( x^2 + 9 ) }}}
{{{ x^4 + 11x^2 + 18 = 0 }}}
OK