If I have $x^4 - 34x^2 + 225 = 0$, is it not possible to to square root both sides of the equation so that I now have $x^2 - 34x + 15$? If this is true, then how would I go about solving the equation from there? I've tried completing the square, but I keep winding up with a large sum not equal to zero when I check my answer. I can't imagine quadratic formula or another method would yield a different result, unless I am going about it wrong.
My professor in their lecture video on this problem instead used the substitution method however, by setting $y = x^2$, and thus $y^2 = x^4$, then replacing all the $x$'s with $y$'s. This method seems to be simply pulling things out of the air though, and doesn't look valid to me. If someone could explain it for me, that would be appreciated as well.
Thank you in advance.