Final answer:
To solve the given polynomial equation, recognize it as a disguised quadratic by letting u = x², then solve for u using the quadratic formula, and finally solve for x.
Step-by-step explanation:
The question asks to solve the polynomial equation f(x) = x⁸ - 34x⁴ + 225. This is a higher degree polynomial equation, but it resembles a quadratic in form if we introduce a substitution, let u = x². Then our equation becomes u² - 34u + 225 which is a quadratic equation in terms of u. Solving this quadratic equation using the quadratic formula (x = [-b ± sqrt(b² - 4ac)] / (2a)) gives us the values for u, which we can then square root to get the values for x.