Example

Solve for $x$: $\quad x^4-37x^2+36=0$

Solution

The substitution $u=x^2$ transforms the equation to quadratic:

The new equation can be solved by factoring:

The quadratic equation has two solutions for the variable $u$, but we are interested in the solutions for the variable $x$. To find those, we must resubstitute and resolve for each $u$-solution.

The original equation has four solutions: $x=-6$, $x=6$, $x=-1$, or $x=1$.