Solving $\cos\pi x +x^2 -6x +10 = 0$

Question

I have the following equation:

$$\cos\pi x +x^2 -6x +10 = 0$$

I have no idea where to begin. I tried taking the derivative multiple times, but it leads to nonsense.

Answer 1

HINTS:
$\cos(\pi x) +x^2 -6x +10 = 0 \implies \cos(\pi x) + (x-3)^2 + 1 = 0$
Since $(x-3)^2\ge 0$ and $\cos(\pi x) \ge -1\ldots $