how to solve an equation by using trial and error method?

𝑇ℎ𝑟𝑜𝑎𝑡 (𝐴∗)=647.5 𝑚𝑚2

A=1027.5 mm^2

How can I calculate 𝑀𝑥 value by using trial and error method or how can I find the value of Mx by another method. Thank you.

Answer 1

[Sam Chak]

@Ali Deniz

I'm not sure what the trial-and-error method is for this, but I think that basic Algebraic methods can be used to rearrange the equation. I followed the example in fzero and make an assumption:

https://www.mathworks.com/help/matlab/ref/fzero.html

% Assume
gamma = 1.55526564459735;

% function to be solved
f = @(M) (1/M)*((2*(1 + (gamma - 1)/2*M^2))/(gamma + 1))^((gamma + 1)/(2*(gamma - 1))) - Ax/Astar;

% initial guess
M0 = 3;

% root-finding solver
Msol = fzero(f, M0)

There should be two real roots.

[Ali Deniz]

Thank you.

-Ali

Answer 2

[Walter Roberson]

Multiply both sides by Mx. Subtract the left side from the right. Expand out. You now have a polynomial of degree 2 in Mx.

[Ali Deniz]

I think you neglect the power of the RHS.

[Walter Roberson]

Ah, I am on mobile. I had tried scrolling the image but it didn't scroll so I didn't see the power.