Solve a*x + x*(b^x) + c = 0

Hello all,

I have troubles while solving equation which is given below symbolically. Could anyone guide me? Thanks in advance.

a*x + x*(b^x) + c = 0

Best regards,

[Birdman]

What have you tried so far? What is your code? Did you search for how to define symbolic variables and symbolic equations? It is really simple.

[Ömer Yaman]

@Birdman

clc
syms x a b c
eqn = a*x+x*(b^x)+c==0;
S=solve(eqn)

Warning: Unable to find explicit solution. For options, see help.

 
S =
 
Empty sym: 0-by-1
 

@Rik

I am sorry but this is not my homework. How can you be so prejudiced.

[Rik]

I appologize. I misread your name and mistook you for another user with a similar name who posted several homework questions and then deleted them.

I applied formatting to your comment and ran your code. The former you can do yourself next time.

[David Goodmanson]

Hi Omer,

It seems highly unlikely that there is an explicit symbolic solution for x. Already the solution to a simpler problem, that of solving

x*exp(x) = z

for x, can only be expressed in terms of the lambertw function, x = lambertw(z). A numerical lambertw function is part of Matlab.

[Ömer Yaman]

@Rik

Thank you for editing!

@David Goodmanson

Thank you, So I guess, I need to instert lambertw function to solve this equation

Answer 1

[Steven Lord]

I'm doubtful that you'll be able to find a general symbolic solution. Substitute numeric values in for a, b, and c and use fzero.