How can I simplify the symbolic expressions?

I hate the fact that solve keeps outputting symbolic expressions with extremely large numbers, when clearly it can simplify further and get rid of those numbers. How can I force it to do that? Its okay with me if I can get an approximation up 6 decimal places.

clear
clc
syms q_bar delta_o theta1 theta2 q S CL_alpha CL_delta b e KT

eqn1 = (2*theta1 - theta2 - q_bar.*theta1 + q_bar.*theta2) == (-0.4805020381.*q_bar.*delta_o);
eqn2 = (-theta1 + theta2 - 2.*q_bar.*theta2) == (-0.0051005137.*q_bar.*delta_o);

sol = solve(eqn1,eqn2,theta1,theta2);

L1 = q.*S.*CL_alpha.*sol.theta1;
L2 = q.*S.*CL_alpha.*sol.theta2 + q.*S.*CL_delta.*delta_o;

eqn1 = (0.25.*L1.*b + 0.75.*L2.*b) == 0;


a=solve(eqn1,q_bar)

a = 

[Torsten]

If you need 6 decimal places, why do you supply model parameters with 10 decimal places ?

-0.4805020381*q_bar
-0.0051005137*q_bar

Answer 1

[John D'Errico]

clear
clc
syms q_bar delta_o theta1 theta2 q S CL_alpha CL_delta b e KT
eqn1 = (2*theta1 - theta2 - q_bar.*theta1 + q_bar.*theta2) == (-0.4805020381.*q_bar.*delta_o);
eqn2 = (-theta1 + theta2 - 2.*q_bar.*theta2) == (-0.0051005137.*q_bar.*delta_o);
sol = solve(eqn1,eqn2,theta1,theta2);
L1 = q.*S.*CL_alpha.*sol.theta1;
L2 = q.*S.*CL_alpha.*sol.theta2 + q.*S.*CL_delta.*delta_o;
eqn1 = (0.25.*L1.*b + 0.75.*L2.*b) == 0;
a=solve(eqn1,q_bar)

a = 

They are simple already. At least, as simple as they can be. You have unknowns in there, inside and outside of the square roots. I suppose you could play around, and make it different, but simpify will not find anything glaring to reduce there.

Can you make the numbers smaller? Well, yes, you can force VPA to round them.

vpa(a,10)

ans = 

Is that simpler? I guess.

[Ali Almakhmari]

Not really. I mean, you can take 5.642719936e17 in common from numerator and denominator and have everything simplify to have all numbers between 0.1 to 10 instead of so complicated like that with high numbers.