simple2_nl.c running 
solve x + 2 x^2 + 3/x = 11.5 
define f(x) = x + 2 x^2 + 3/x - 11.5 
derivative fp(x) = 1.0 + 4.0*x - 6.0/(x*x) 
guess initial x 
iterate x_next = x - f(x)/fp(x) 
no guarentee of solution or unique solution 
f(x) should go to zero 
x=  3.0000, f(x)= 10.5000, fp(x)= 12.3333, f/fp=  0.8514, x_next=  2.1486 
x=  2.1486, f(x)=  1.2783, fp(x)=  8.2950, f/fp=  0.1541, x_next=  1.9945 
x=  1.9945, f(x)= -0.0449, fp(x)=  7.4700, f/fp= -0.0060, x_next=  2.0006 
x=  2.0006, f(x)=  0.0046, fp(x)=  7.5031, f/fp=  0.0006, x_next=  1.9999 
x=  1.9999, f(x)= -0.0005, fp(x)=  7.4997, f/fp= -0.0001, x_next=  2.0000 
x=  2.0000, f(x)=  0.0000, fp(x)=  7.5000, f/fp=  0.0000, x_next=  2.0000 

new initial guess
x=  1.5000, f(x)= -3.5000, fp(x)=  4.3333, f/fp= -0.8077, x_next=  2.3077 
x=  2.3077, f(x)=  2.7586, fp(x)=  9.1041, f/fp=  0.3030, x_next=  2.0047 
x=  2.0047, f(x)=  0.0387, fp(x)=  7.5258, f/fp=  0.0051, x_next=  1.9995 
x=  1.9995, f(x)= -0.0038, fp(x)=  7.4975, f/fp= -0.0005, x_next=  2.0000 
x=  2.0000, f(x)=  0.0004, fp(x)=  7.5003, f/fp=  0.0001, x_next=  2.0000 
x=  2.0000, f(x)= -0.0000, fp(x)=  7.5000, f/fp= -0.0000, x_next=  2.0000 

new initial guess
x=  2.1000, f(x)=  0.8486, fp(x)=  8.0395, f/fp=  0.1056, x_next=  1.9944 
x=  1.9944, f(x)= -0.0457, fp(x)=  7.4694, f/fp= -0.0061, x_next=  2.0006 
x=  2.0006, f(x)=  0.0047, fp(x)=  7.5031, f/fp=  0.0006, x_next=  1.9999 
x=  1.9999, f(x)= -0.0005, fp(x)=  7.4997, f/fp= -0.0001, x_next=  2.0000 
x=  2.0000, f(x)=  0.0000, fp(x)=  7.5000, f/fp=  0.0000, x_next=  2.0000 
x=  2.0000, f(x)= -0.0000, fp(x)=  7.5000, f/fp= -0.0000, x_next=  2.0000 

new initial guess
x=  2.0000, f(x)=  0.0000, fp(x)=  7.5000, f/fp=  0.0000, x_next=  2.0000 
x=  2.0000, f(x)=  0.0000, fp(x)=  7.5000, f/fp=  0.0000, x_next=  2.0000 
x=  2.0000, f(x)=  0.0000, fp(x)=  7.5000, f/fp=  0.0000, x_next=  2.0000 
x=  2.0000, f(x)=  0.0000, fp(x)=  7.5000, f/fp=  0.0000, x_next=  2.0000 
simple2_nl.c running