Note that
a² - b² = (a+b)(a-b)
i² = -1 by definition.
We want to factorize x² + 36 = x² + 6².
Consider the expression
x² - (6i)² = x² - (6²)(i²) = x² - 36i² = x² + 36
Because x² - (6i)² = (x + 6i)(x - 6i)
Therefore
x² + 36 = (x + 6i)(x - 6i)
Answer: (x + 6i)(x - 6i)