Let's simplify the equation step by step.

First, simplify the left side of the equation:
√x^2 x^2 + 12x + 36 = x^2 x^2 + 12x + 36 = x^4 + 12x + 36

Now, simplify the right side of the equation:
x^2 - 36

Now, set the left side of the equation equal to the right side and solve for x:
x^4 + 12x + 36 = x^2 - 36
x^4 + 12x + 36 - x^2 + 36 = 0
x^4 - x^2 + 12x + 72 = 0

Unfortunately, this equation cannot be easily solved using standard algebraic methods. You may need to use numerical or graphical methods to find the approximate solutions for x.