Question

X^4-x^2-42=0 need to solve equation and find solution set

Answer 1

That's a quadratic equation in $x^2$, which means we get an extra square root and $\pm$ at the end.

$x^4 - x^2 - 42 = 0$

We factor,

$(x^2 - 7)(x^2+6) = 0$

$x^2 = 7 \quad \textrm{or} \quad x^2 = -6$

$x = \pm \sqrt{7} \quad \textrm{or} \quad x = \pm i \sqrt{6}$