When $z+2yx+x^2$ is a perfect square?

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I got two big integers $z$ and $y$ where $gcd(z,y) = 1$ $$z+2yx+x^2$$

How to find when f(x) = $z+2yx+x^2$ is a perfect squere for positive integer $x$?

Is this problem is as hard as Integer factorization problem? If it is, how can it be transformed into the form of:

$$a^2 = b^2 mod(c)$$

So optimizations like Dixon's factorization could be applied