How to solve nonlinear equation: $$x+2.1*\frac{100}{1+e^{(10-q(x))/3}}-2=0,\\ here \quad q(x)=\frac{100}{1+e^{(10-x)/3}}$$ Are here any numerical method suitable to solve or any package? I tried Newton method, but didn't get a right answer.
2026-03-29 16:18:50.1774801130
Solve nonlinear equation
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I really do not see what kind of problems you could have faced with Newton method.
Using the values of $x_0$ you used, below are given the iterates $$\left( \begin{array}{cc} n & x_n \\ 0 & 0 \\ 1 & -2.3881246 \\ 2 & -4.9553903 \\ 3 & -6.1937576 \\ 4 & -6.3118065 \\ 5 & -6.3125527 \end{array} \right)$$
$$\left( \begin{array}{cc} n & x_n \\ 0 & +1.0000000 \\ 1 & -1.1036705 \\ 2 & -3.7121240 \\ 3 & -5.7946726 \\ 4 & -6.2973982 \\ 5 & -6.3125408 \\ 6 & -6.3125527 \end{array} \right)$$