# Solve a nonlinear equation **URL:** \ **Category:** Questions\ **Tags:** computer-science, engineering, physics, mathematica\ **Created:** [November 11, 2015, 2:31pm UTC](https://community.wolfram.com/t/solve-a-nonlinear-equation/7176 "2015-11-11T14:31:29Z")\ **Posts on this page:** 10\ **Page:** 1
**Author:** ![minhngocvu](https://avatars.discourse-cdn.com/v4/letter/m/7ba0ec/32.png) [@minhngocvu](https://community.wolfram.com/u/minhngocvu)\ **Post date:** [November 11, 2015, 2:31pm UTC](https://community.wolfram.com/t/solve-a-nonlinear-equation/7176/1 "2015-11-11T14:31:29Z")
Hi everyone, I wanna to solve the equation below. Could you please show me how I can write the commands in the Mathematica. Thank you in advance, The equation is : NSolve[x^5 - A[i]\*x - 1 ==0,x] where A[i] = i/10, {i=1,10,1] ---
**Author:** ![fkampas](https://yyz1.discourse-cdn.com/wolfram/user_avatar/community.wolfram.com/fkampas/32/41217_2.png) [@fkampas](https://community.wolfram.com/u/fkampas)\ **Post date:** [November 11, 2015, 2:45pm UTC](https://community.wolfram.com/t/solve-a-nonlinear-equation/7176/2 "2015-11-11T14:45:19Z")
In[13]:= a = Range[10]/10 ``` Out[13]= {1/10, 1/5, 3/10, 2/5, 1/2, 3/5, 7/10, 4/5, 9/10, 1} In[14]:= Table[NSolve[x^5 - a[[i]]*x - 1 == 0, x], {i, 10}] Out[14]= {{{x -> -0.802967 - 0.568379 I}, {x -> -0.802967 + 0.568379 I}, {x -> 0.293163 - 0.96304 I}, {x -> 0.293163 + 0.96304 I}, {x -> 1.01961}}, {{x -> -0.797202 - 0.548183 I}, {x -> -0.797202 + 0.548183 I}, {x -> 0.27797 - 0.975447 I}, {x -> 0.27797 + 0.975447 I}, {x -> 1.03846}}, {{x -> -0.79176 - 0.527168 I}, {x -> -0.79176 + 0.527168 I}, {x -> 0.263454 - 0.988232 I}, {x -> 0.263454 + 0.988232 I}, {x -> 1.05661}}, {{x -> -0.786675 - 0.5053 I}, {x -> -0.786675 + 0.5053 I}, {x -> 0.249625 - 1.00134 I}, {x -> 0.249625 + 1.00134 I}, {x -> 1.0741}}, {{x -> -0.781977 - 0.482538 I}, {x -> -0.781977 + 0.482538 I}, {x -> 0.236492 - 1.01473 I}, {x -> 0.236492 + 1.01473 I}, {x -> 1.09097}}, {{x -> -0.77769 - 0.458827 I}, {x -> -0.77769 + 0.458827 I}, {x -> 0.22406 - 1.02834 I}, {x -> 0.22406 + 1.02834 I}, {x -> 1.10726}}, {{x -> -0.77383 - 0.434095 I}, {x -> -0.77383 + 0.434095 I}, {x -> 0.212328 - 1.04213 I}, {x -> 0.212328 + 1.04213 I}, {x -> 1.123}}, {{x -> -0.770409 - 0.408237 I}, {x -> -0.770409 + 0.408237 I}, {x -> 0.201289 - 1.05602 I}, {x -> 0.201289 + 1.05602 I}, {x -> 1.13824}}, {{x -> -0.767428 - 0.381103 I}, {x -> -0.767428 + 0.381103 I}, {x -> 0.19093 - 1.06998 I}, {x -> 0.19093 + 1.06998 I}, {x -> 1.153}}, {{x -> -0.764884 - 0.352472 I}, {x -> -0.764884 + 0.352472 I}, {x -> 0.181232 - 1.08395 I}, {x -> 0.181232 + 1.08395 I}, {x -> 1.1673}}} ``` ---
**Author:** ![seanc](https://yyz1.discourse-cdn.com/wolfram/user_avatar/community.wolfram.com/seanc/32/34005_2.png) [@seanc](https://community.wolfram.com/u/seanc)\ **Post date:** [November 11, 2015, 2:47pm UTC](https://community.wolfram.com/t/solve-a-nonlinear-equation/7176/3 "2015-11-11T14:47:07Z")
First, define the function “A”. I strongly recommend creating more expressive names than this. ``` A[i_] := i/10 ``` Use Table to create a list of functions ``` Table[x^5 - A[i]*x - 1 == 0, {i, 1 , 10}] ``` Tables like this can be used with NSolve. The set of equations may or may not have a solution. ---
**Author:** ![minhngocvu](https://avatars.discourse-cdn.com/v4/letter/m/7ba0ec/32.png) [@minhngocvu](https://community.wolfram.com/u/minhngocvu)\ **Post date:** [November 11, 2015, 3:29pm UTC](https://community.wolfram.com/t/solve-a-nonlinear-equation/7176/4 "2015-11-11T15:29:22Z")
Dear Sean Clarke, According to your help, I wrote the following commands but I think it does not work. Can you explain me please. (Debug) In[28]:= NSolve[x^5 - x/10 - 1 == 0, x, Reals] (Debug) Out[28]= {{x → 1.01961}} (Debug) In[29]:= NSolve[x^5 - x/5 - 1 == 0, x, Reals] (Debug) Out[29]= {{x → 1.03846}} (Debug) In[30]:= NSolve[x^5 - 3 x/10 - 1 == 0, x, Reals] (Debug) Out[30]= {{x → 1.05661}} (Debug) In[31]:= NSolve[x^5 - 2 x/5 - 1 == 0, x, Reals] (Debug) Out[31]= {{x → 1.0741}} (Debug) In[43]:= Clear[x]; A[i\_] := i/10; Table[NSolve[x^5 - 2 x/5 - 1 == 0, x, Reals], {i, 1, 5}] (Debug) During evaluation of In[43]:= SetDelayed::write: Tag List in {1/10,1/5,3/10,2/5,1/2,3/5,7/10,4/5,9/10,1}[i\_] is Protected. \>\> (Debug) Out[45]= {{{x → 1.0741}}, {{x → 1.0741}}, {{x → 1.0741}}, {{x → 1.0741}}, {{x → 1.0741}}} ---
**Author:** ![seanc](https://yyz1.discourse-cdn.com/wolfram/user_avatar/community.wolfram.com/seanc/32/34005_2.png) [@seanc](https://community.wolfram.com/u/seanc)\ **Post date:** [November 11, 2015, 4:21pm UTC](https://community.wolfram.com/t/solve-a-nonlinear-equation/7176/5 "2015-11-11T16:21:12Z")
You are using “A” as a variable name. I strongly suggest changing the name of it. Single letter variable or function names are a bad idea. The error message is complaining that “A” is already defined. Try running your code in a clean kernel. That is, run Quit and then try running the code. ---
**Author:** ![minhngocvu](https://avatars.discourse-cdn.com/v4/letter/m/7ba0ec/32.png) [@minhngocvu](https://community.wolfram.com/u/minhngocvu)\ **Post date:** [November 11, 2015, 6:53pm UTC](https://community.wolfram.com/t/solve-a-nonlinear-equation/7176/6 "2015-11-11T18:53:01Z")
It works :). Thank you very much. After, Is it possible to print x[i] and A[i] by two colones as? A[1] x[1] A[2] x[2] … A[10] x[10] ---
**Author:** ![seanc](https://yyz1.discourse-cdn.com/wolfram/user_avatar/community.wolfram.com/seanc/32/34005_2.png) [@seanc](https://community.wolfram.com/u/seanc)\ **Post date:** [November 11, 2015, 7:41pm UTC](https://community.wolfram.com/t/solve-a-nonlinear-equation/7176/7 "2015-11-11T19:41:35Z")
You can modify the Table command: ``` Table[{A[i], NSolve[x^5 - 2 x/5 - 1 == 0, x, Reals]}, {i, 1, 5}] ``` ---
**Author:** ![minhngocvu](https://avatars.discourse-cdn.com/v4/letter/m/7ba0ec/32.png) [@minhngocvu](https://community.wolfram.com/u/minhngocvu)\ **Post date:** [November 11, 2015, 9:06pm UTC](https://community.wolfram.com/t/solve-a-nonlinear-equation/7176/8 "2015-11-11T21:06:02Z")
But Is it possible to write x[i] as a table like [x[1],x[2],…,x[5]]. Because actually it gives: {{{x → 1.01961}}, {{x → 1.03846}}, {{x → 1.05661}}, {{x → 1.0741}}, {{x → 1.09097}}} I wanna only :{1.01961,1.03846,1.05661,1.0741,1.09097} Thank you in advance, ---
**Author:** ![minhngocvu](https://avatars.discourse-cdn.com/v4/letter/m/7ba0ec/32.png) [@minhngocvu](https://community.wolfram.com/u/minhngocvu)\ **Post date:** [November 12, 2015, 9:19am UTC](https://community.wolfram.com/t/solve-a-nonlinear-equation/7176/9 "2015-11-12T09:19:50Z")
Dear, Could you show me how I can write the solution under format: {x[1], x[2], x[3], x[4], x[5]} after solving the following equation Thank you in advance A[i\_] := i/10 Table[NSolve[x^5 - A[i]x/ - 1 == 0, x, Reals], {i, 1, 5}] The results are: {{{x → 1.01961}}, {{x → 1.03846}}, {{x → 1.05661}}, {{x → 1.0741}}, {{x → 1.09097}}} But I want to write only {1.01961, 1.03846, 1.05661, 1.0741, 1.09097} to faciliate the copy and paste in excel ---
**Author:** ![fkampas](https://yyz1.discourse-cdn.com/wolfram/user_avatar/community.wolfram.com/fkampas/32/41217_2.png) [@fkampas](https://community.wolfram.com/u/fkampas)\ **Post date:** [November 12, 2015, 2:38pm UTC](https://community.wolfram.com/t/solve-a-nonlinear-equation/7176/10 "2015-11-12T14:38:27Z")
In[1]:= A[i\_] := i/10 In[6]:= Table[{A[i], x /. NSolve[x^5 - 2 A[i]\*x - 1 == 0, x, Reals][[1]]}, {i, 1, 10}] Out[6]= {{1/10, 1.03846}, {1/5, 1.0741}, {3/10, 1.10726}, {2/5, 1.13824}, {1/2, 1.1673}, {3/5, 1.19468}, {7/10, 1.22055}, {4/5, 1.24508}, {9/10, -0.918257}, {1, -1.}}