Question 856859
Make the substitution:
{{{ z = x^2 }}}
and
{{{ z^2 = x^4 }}}
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{{{ z^2 - 32z - 256 = 0 }}}
{{{ z = ( -b +- sqrt( b^2 - 4*a*c )) / (2*a) }}}
{{{ a = 1 }}}
{{{ b = -32 }}}
{{{ c = -256 }}}
{{{ z = ( -(-32) +- sqrt( (-32)^2 - 4*1*(-256) )) / (2*1) }}}
{{{ z = ( 32 +- sqrt( 1024 + 1024 )) / 2 }}}
{{{ z = ( 32 +- sqrt( 2048 )) / 2 }}}
{{{ z = ( 32 +- 32*sqrt(2)) / 2 }}}
{{{ z = 16*( 1 + sqrt(2) ) }}}
{{{ z = 16*( 1 - sqrt(2) ) }}}
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{{{ z = x^2 }}}
{{{ x = sqrt(z) }}}
{{{ x = -sqrt(z) }}}
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{{{ x = 4*sqrt( 1 + sqrt(2) ) }}}
{{{ x = -4*sqrt( 1 + sqrt(2) ) }}}
{{{ x = 4*sqrt( 1 - sqrt(2) ) }}} ( imaginary root )
{{{ x = -4*sqrt( 1 - sqrt(2) ) }}} ( imaginary root )
You can plug these back in to check