Solving for d in an equation and verifying with free software

Mech_LS24 · Aug 27, 2022

Dear mathematicians,

I am getting stuck solving this equation for "d". And what (free)software would you recommend to check this equation?

Handwritten heading "Solve for d:" above the equation 400·10^6 = 0.5 · (5.96 / ((π/32)·((0.033^4 − d^4)/0.033))) + 0.5 · sqrt((5.96 / ((π/32)·((0.033^4 − d^4)/0.033)))^2 + 4·(61/((π/4)·(0.033^2 − d^2)))^2).

Typeset equation: 400·10^6 = 0.5·(5.96 / ((π/32)·((0.033^4 − d^4)/0.033))) + 0.5·√((5.96 / ((π/32)·((0.033^4 − d^4)/0.033)))^2 + 4·(61 / ((1/4)·π·(0.033^2 − d^2)))^2)

Thanks a lot!

malawi_glenn · Aug 27, 2022

Use desmos or something or wolfram alpha

topsquark · Aug 27, 2022

Mech_LS24 said:

Summary: I would like to solve the equation for "d".

Dear mathematicians,

I am getting stuck solving this equation for "d". And what (free)software would you recommend to check this equation?
View attachment 313333

View attachment 313334

Thanks a lot!

Unless something cancels it's going to be a 10th order polynomial. And given your numbers it's highly unlikely to be factorable. W|A, Mathematica, or Matlab would be my suggestions.

-Dan

fresh_42 · Aug 27, 2022

If you really want to attack that expression, I recommend the substitutions ##x=0.033^2 -d^2 ## and ##y=0.033^2+d^2##. And you should consider using a Weierstraß substitution!

Solving for d in an equation and verifying with free software

Discussion

Similar threads