POLYMATH Report          NLE 
 Nonlinear Equation 2016-May-30 

Calculated values of NLE variables
    Variable Value f(x) Initial Guess Initial f(x)
1 x 20 4.3E-11 50.05 8.5E03

    Variable Value Initial Value
1 t 20 69.9886

Nonlinear equations
1 f(x) = t + 4*x^2 - 1620 = 0

Explicit equations
1 t = x*log(x/2)

Problem source text
# S. 6 - Single NLE
# Solve the nonlinear equation
# x*log(x/2)+4*x^2 = 1620
#Verified Solution x = 20
f(x) = t + 4*x^2 - 1620
t = x*log(x/2)
x(min) = 0.1
x(max) = 100

Matlab formatted problem
Create m file called PolyNle.m and paste the following text into it.
% S. 6 - Single NLE
% Solve the nonlinear equation
% x*log(x/2)+4*x^2 = 1620
% Verified Solution x = 20
function PolyNle
   xguess = 50.05 ;
   x = fzero(@NLEfun,xguess);
   fprintf('The NLE solution is %g\n', x);
end

function fx = NLEfun(x)
   t = x * log10(x / 2);
   fx = t + 4 * x ^ 2 - 1620;
end

Root function values
  x f(x)
1 0.1 -1620.09
2 2.13878 -1601.64
3 4.17755 -1548.86
4 6.21633 -1462.37
5 8.2551 -1342.33
6 10.2939 -1188.82
7 12.3327 -1001.88
8 14.3714 -781.539
9 16.4102 -527.821
10 18.449 -240.738
11 20.4878 79.6946
12 22.5265 433.469
13 24.5653 820.576
14 26.6041 1241.01
15 28.6429 1694.76
16 30.6816 2181.83
17 32.7204 2702.22
18 34.7592 3255.91
19 36.798 3842.9
20 38.8367 4463.2
21 40.8755 5116.79
22 42.9143 5803.69
23 44.9531 6523.88
24 46.9918 7277.36
25 49.0306 8064.13
26 51.0694 8884.19
27 53.1082 9737.54
28 55.1469 1.06E+04
29 57.1857 1.15E+04
30 59.2245 1.25E+04
31 61.2633 1.35E+04
32 63.302 1.45E+04
33 65.3408 1.56E+04
34 67.3796 1.66E+04
35 69.4184 1.78E+04
36 71.4571 1.89E+04
37 73.4959 2.01E+04
38 75.5347 2.13E+04
39 77.5735 2.26E+04
40 79.6122 2.39E+04
41 81.651 2.52E+04
42 83.6898 2.65E+04
43 85.7286 2.79E+04
44 87.7673 2.93E+04
45 89.8061 3.08E+04
46 91.8449 3.23E+04
47 93.8837 3.38E+04
48 95.9224 3.53E+04
49 97.9612 3.69E+04
50 100 3.85E+04

General Settings
Total number of equations 2
Number of implicit equations 1
Number of explicit equations 1
Elapsed time 0.04 sec
Reporting digits 8
Solution method safenewt
Max iterations 150
Tolerance F 1E-07
Tolerance X 1E-07
Tolerance min 1E-07