Question 1067896
{{{ 2x^4 - 5x^2 - 7 = 0 }}}
make the substitutions:
{{{ z = x^2 }}}
and
{{{ z^2 = x^4 }}}
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{{{ 2z^2 - 5z - 7 = 0 }}}
Use the quadratic formula
{{{ z = ( -b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{ a = 2 }}}
{{{ b = -5 }}}
{{{ c = -7 }}}
{{{ z = ( -(-5) +- sqrt( (-5)^2-4*2*(-7) ))/(2*2) }}}
{{{ z = ( 5 +- sqrt( 25 + 56 ))/4 }}}
{{{ z = ( 5 +-sqrt( 81 )) / 4 }}}
{{{ z = ( 5 + 9 ) / 4 }}}
{{{ z = 7/2 }}}
and
{{{ z = ( 5 - 9 )/4 }}}
{{{ z = -1 }}}
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{{{ z = x^2 }}}
{{{ x = sqrt(z) }}}
{{{ x = sqrt( 7/2 ) }}}
{{{ x = -sqrt( 7/2 ) }}}
and
{{{ x = sqrt(-1) }}}
{{{ x = -sqrt(-1) }}}
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These are the 4 answers,  2 of which are imaginary
You can check them by plugging into given equation
Here's the plot:
{{{ graph( 400, 400, -4, 4, -15, 5, 2x^4 - 5x^2 - 7 ) }}}
Looks close since {{{ sqrt( 7/2 ) = 1.87 }}}