Determinate all the positive integers $x$ such that $x^4+6x^3+11x^2+3x+11$ is a perfect square.
My try
With pure intuition I can say that there is no $ x $ that meets this condition, i tried by brute force some numbers and none worked, but I would like to know if what I'm guessing is right or not, and what would be a way to prove it, because i don't see the way to prove this.