Question 166175
{{{-x^4+200=102x^2}}}
{{{-x^4-102x^2+200=0}}}
{{{x^4+102x^2-200=0}}}
Looks kind of like a quadratic equation.
Use a substitution. 
{{{u=x^2}}}
{{{x^4+102x^2-200=0}}}
{{{u^2+102u-200=0}}}
Now solve using the quadratic formula,
{{{u = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}}
{{{u = (-102 +- sqrt( 102^2-4*1*(-200) ))/(2*1) }}}
{{{u = (-102 +- sqrt( 10404+800 ))/(2) }}}
{{{u = (-102 +- sqrt(11204))/(2) }}}
{{{u = (-102 +- 105.85)/(2) }}}
Let's look at both solutions separately,
{{{u[1] = (-102 + 105.85)/(2) }}}
{{{u[1] = (3.85)/(2) }}}
{{{u[1] = 1.925 }}}
{{{(x)^2 = 1.925 }}}
{{{x= 0 +- 1.387}}}
{{{x[1]= 1.387}}}
{{{x[2]= -1.387}}}
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{{{u[2] = (-102 - 105.85)/(2) }}}
{{{u[2] = (-207.85)/(2) }}}
{{{u[2] = -103.925}}}
{{{(x)^2 = -103.925}}}
{{{x= 0 +- 10.19i}}}
{{{x[3]= 10.19i}}}
{{{x[4]= -10.19i}}}