Question 61784
{{{x^4 + 1 = 6x^2}}}
{{{x^4 - 6x^2 + 1 = 0}}}
solve by completing the square
If b is the coefficient of {{{x^2}}},
then {{{x^4 - bx^2 + (b/2)^2 = 0}}}
First subtract 1 from both sides
{{{x^4 - 6x^2 = -1}}}
{{{x^4 - 6x^2 + 9 = - 1 + 9}}}
{{{(x^2 - 3)^2 = 8}}}
take the square root of both sides
{{{x^2 - 3 = 2*(0+-sqrt(2))}}}
{{{x^2 = 3 + 2sqrt(2)}}} and
{{{x^2 = 3 - 2sqrt(2)}}}
solving for x
{{{x = + sqrt(3 + 2sqrt(2))}}}
{{{x = - sqrt(3 + 2sqrt(2))}}}
{{{x = + sqrt(3 - 2sqrt(2))}}}
{{{x = - sqrt(3 - 2sqrt(2))}}}
Try each of these. I tried one, and 
it was a solution