1111
1212import math
1313from decimal import *
14- getcontext ().prec = 15
15- 16- x = Decimal (input ("Enter a number: " ))
17- z = Decimal (input ("Sqrt guess: " ))
18- 19- print ("Math.sqrt(x): \t \t " + str (Decimal (math .sqrt (x )))) # Accurate sqrt
20- 14+ getcontext ().prec = 15 # Changing precision of answer, goes to 15 decimal points
15+ 16+ # Probably an easier way to error-handle this but it works.
17+ startZ = False # Can't get z without getting x first
18+ start = False # When user has correctly entered both x and z, start the rest
19+ 20+ while startZ == False :
21+ try :
22+ x = float (input ("Enter a number: " ))
23+ while x < 1 :
24+ print ("Please enter a positive number!" )
25+ x = float (input ())
26+ startZ = True
27+ 28+ except ValueError :
29+ print ("Please only enter number values, try again." )
30+ 31+ while start == False :
32+ try :
33+ z = float (input ("Sqrt guess: " ))
34+ start = True
35+ except ValueError :
36+ print ("Please only enter number values, try again." )
37+ 38+ # Print answer using built-in math.sqrt function
39+ # Convert to Decimal for more accuracy, also get the absolute values in case user entered negative num
40+ # Abs function adapted from https://www.tutorialspoint.com/python/number_abs.htm
41+ print ("Math.sqrt(x): \t \t " + str (Decimal (math .sqrt (abs (x ))))) # Accurate sqrt
42+ 43+ # Convert x and z to Decimals
44+ x = Decimal (abs (x ))
45+ z = Decimal (abs (z ))
46+ 47+ # Do the first calculation
2148approximate = z - ((z * z - x ) / (2 * z ))
22- difference = 1
23- count = 1 # Calculation done once
49+ difference = 1 # Init the difference in answers at 1 - if init at 0, while loop won't run
50+ count = 1 # Calculation already done once
2451
2552while difference > 0.00000000001 :
26- z = approximate
53+ z = approximate # set new z to be last answer
2754 approximate = z - ((z * z - x ) / (2 * z ))
28- difference = z - approximate
55+ difference = z - approximate # Keep track of difference between z and approx
2956 count = count + 1
3057
3158print ("Newton's Method: \t " + str (approximate ) + " (" + str (count ) + " iterations)" )
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