Solving x^4 - x^2 = k for x: Tips and Tricks to Simplify Equations

[Ted123]

Solve the equation $$x^4 - x^2 = k$$ where $k>0$.

Am I being thick or how do I solve this for $x$?

Factorising gives $$x^2(x^2-1)=k$$ but now where?

 

[HallsofIvy]

Let $y= x^2$ and that becomes a quadratic function:
$y^2- y= k$ or $y^2- y- k= 0$. Solve that for y, then solve $x^2= y$ for x.