SOLUTION: Hi, I am studying for a test and could really use some help with this problem. I know that I can use either the quadratic equation, completing the square, or factoring. {{{x^2+m^2

You can put this solution on YOUR website!
You're on the right track, we're going to complete the square
subtract 2mx from both sides (edit: sorry you're not supposed to subtract m^2 on the left hand side)
Now we need to find 2 terms which add to -2mx and multiply to m^2, these two are -m and -m, so the factors are

Which can be also written as this
Take square root of both sides
Subtract nx and add m to both sides
Factor out an x
Divide both sides by (1-n)

To verify this let m and n be any numbers (preferably small numbers to make it easy) and this should be equivalent to the given problem.
Check let m=1, n=2, and plug in x=1


So the answer checks out