Here’s an expanded version of what I posted. Not a good way of doing it, but I can’t think of another way to solve your problem with the given constraints.

find absolute value of input x: square x and then use an approximation method to find the square root of the square of x

for z[sub]0[/sub], choose a value as close to x as possible to converge quickly. In my case, I just make a crappy guess, z[sub]0[/sub] = 2

z[sub]0[/sub] = 2

z[sub]n+1[/sub] = ((z[sub]n[/sub] + (x[sup]2[/sup] / z[sub]n[/sub])) / 2)

so, expanding:

z[sub]1[/sub] = ((z[sub]0[/sub] + (x[sup]2[/sup] / z[sub]0[/sub])) / 2)

z[sub]2[/sub] = ((((z[sub]0[/sub] + (x[sup]2[/sup] / z[sub]0[/sub])) / 2) + (x[sup]2[/sup] / ((z[sub]0[/sub] + (x[sup]2[/sup] / z[sub]0[/sub])) / 2))) / 2)

z[sub]3[/sub] = ((((((z[sub]0[/sub] + (x[sup]2[/sup] / z[sub]0[/sub])) / 2) + (x[sup]2[/sup] / ((z[sub]0[/sub] + (x[sup]2[/sup] / z[sub]0[/sub])) / 2))) / 2) + (x[sup]2[/sup] / ((((z[sub]0[/sub] + (x[sup]2[/sup] / z[sub]0[/sub])) / 2) + (x[sup]2[/sup] / ((z[sub]0[/sub] + (x[sup]2[/sup] / z[sub]0[/sub])) / 2))) / 2))) / 2)

z[sub]4[/sub] = ((((((((z[sub]0[/sub] + (x[sup]2[/sup] / z[sub]0[/sub])) / 2) + (x[sup]2[/sup] / ((z[sub]0[/sub] + (x[sup]2[/sup] / z[sub]0[/sub])) / 2))) / 2) + (x[sup]2[/sup] / ((((z[sub]0[/sub] + (x[sup]2[/sup] / z[sub]0[/sub])) / 2) + (x[sup]2[/sup] / ((z[sub]0[/sub] + (x[sup]2[/sup] / z[sub]0[/sub])) / 2))) / 2))) / 2) + (x[sup]2[/sup] / ((((((z[sub]0[/sub] + (x[sup]2[/sup] / z[sub]0[/sub])) / 2) + (x[sup]2[/sup] / ((z[sub]0[/sub] + (x[sup]2[/sup] / z[sub]0[/sub])) / 2))) / 2) + (x[sup]2[/sup] / ((((z[sub]0[/sub] + (x[sup]2[/sup] / z[sub]0[/sub])) / 2) + (x[sup]2[/sup] / ((z[sub]0[/sub] + (x[sup]2[/sup] / z[sub]0[/sub])) / 2))) / 2))) / 2))) / 2)

z[sub]5[/sub] = ((((((((((z[sub]0[/sub] + (x[sup]2[/sup] / z[sub]0[/sub])) / 2) + (x[sup]2[/sup] / ((z[sub]0[/sub] + (x[sup]2[/sup] / z[sub]0[/sub])) / 2))) / 2) + (x[sup]2[/sup] / ((((z[sub]0[/sub] + (x[sup]2[/sup] / z[sub]0[/sub])) / 2) + (x[sup]2[/sup] / ((z[sub]0[/sub] + (x[sup]2[/sup] / z[sub]0[/sub])) / 2))) / 2))) / 2) + (x[sup]2[/sup] / ((((((z[sub]0[/sub] + (x[sup]2[/sup] / z[sub]0[/sub])) / 2) + (x[sup]2[/sup] / ((z[sub]0[/sub] + (x[sup]2[/sup] / z[sub]0[/sub])) / 2))) / 2) + (x[sup]2[/sup] / ((((z[sub]0[/sub] + (x[sup]2[/sup] / z[sub]0[/sub])) / 2) + (x[sup]2[/sup] / ((z[sub]0[/sub] + (x[sup]2[/sup] / z[sub]0[/sub])) / 2))) / 2))) / 2))) / 2) + (x[sup]2[/sup] / ((((((((z[sub]0[/sub] + (x[sup]2[/sup] / z[sub]0[/sub])) / 2) + (x[sup]2[/sup] / ((z[sub]0[/sub] + (x[sup]2[/sup] / z[sub]0[/sub])) / 2))) / 2) + (x[sup]2[/sup] / ((((z[sub]0[/sub] + (x[sup]2[/sup] / z[sub]0[/sub])) / 2) + (x[sup]2[/sup] / ((z[sub]0[/sub] + (x[sup]2[/sup] / z[sub]0[/sub])) / 2))) / 2))) / 2) + (x[sup]2[/sup] / ((((((z[sub]0[/sub] + (x[sup]2[/sup] / z[sub]0[/sub])) / 2) + (x[sup]2[/sup] / ((z[sub]0[/sub] + (x[sup]2[/sup] / z[sub]0[/sub])) / 2))) / 2) + (x[sup]2[/sup] / ((((z[sub]0[/sub] + (x[sup]2[/sup] / z[sub]0[/sub])) / 2) + (x[sup]2[/sup] / ((z[sub]0[/sub] + (x[sup]2[/sup] / z[sub]0[/sub])) / 2))) / 2))) / 2))) / 2))) / 2)

etc.