Question 828144
{{{x^4 - 29x^2 + 100 = 0}}} may look difficult,
but I bet you could solve {{{y^2 - 29y + 100 = 0}}} somehow.
If you look closely, you will notice that making {{{y=x^2}}} you get {{{y^2=x^4}}},
and substituting those expressions one equation turns into the other equation.
 
I would solve {{{y^2 - 29y + 100 = 0}}} by factoring:
{{{y^2 - 29y + 100 = 0}}}
{{{(y-4)(y-25)=0}}} --> {{{system(highlight(y=4),"or",highlight(y=25))}}}
Maybe you would solve it by applying the quadratic formula:
{{{y=(-(-29) +- sqrt((-29)^2-4*1*100 ))/(2*1) }}}
{{{y=(29 +- sqrt(841-400))/2}}}
{{{y=(29 +- sqrt(441))/2}}}
{{{y=(29 +- 21)/2}}} --> {{{system(y=(29-21)/2=8/2=highlight(4),"or",y=(29+21)/2=50/2=highlight(25))}}} 
 
Either way you end up with
{{{x^2=4}}} --> {{{system(highlight(x=-2),"or",highlight(x=2))}}}
or
{{{x^2=25}}} --> {{{system(highlight(x=-5),"or",highlight(x=5))}}}
 
The short way to write the solution to the equation is:
{{{x^4 - 29x^2 + 100 = 0}}}
{{{(x^2-4)(x^2-25)=0}}}
{{{(x-2)(x+2)(x-5)(x+5)=0}}} --> {{{system(highlight(x=-2),"or",highlight(x=2),"or",highlight(x=-5),"or",highlight(x=5))}}}