What do you mean by "solve" it? There exist an infinite set of values that will solve it. With one equation in 17 variables, the best you can do is solve for one of the variables in terms of the other 16.
I need to solve the following equation for "R." All variables are single letters. Please help, I've been working at it for days now and just can't get it
I+(O*M*K*R*T) =
{J*[(A/B)+((C-D)/B)]*{[(E*B)+(N*M*G*T*B*R)-(F*A)]/[F(C-D)-B(G-H)]}} - {(K-L)*[(E*B)+(N*M*G*T*B*R)-(B*A)]/[F(C-D)-B(G-H)]}
I know that's hell to read. Any suggestions of a better way to present it would be much apprecaited. Please feel free to ask questions if you need clarification.
Thank you SO SO SO much!
Cheers,
ChemOsh
What do you mean by "solve" it? There exist an infinite set of values that will solve it. With one equation in 17 variables, the best you can do is solve for one of the variables in terms of the other 16.
your equation becomes easier to read if you replace formulas that don't involve R with a single letter. for example, let:
S = J*[(A/B)+(C-D)/B)]
U = N*M*G*T*B
V = F(C-D) - B(G-H)
W = O*M*K*T (assuming multiplication is commutative, so R*T = T*R)
this gives us I + W*R = S*[(E-B) + U*R - (F*A)]/V - (K-L)*[(E-B) + U*R - (B*A)]/V
so W*R = (S*U)*R/V - [(K-L)*U]*R/V + (S*(E-B))/V - [S*(F*A)]/V - [(K-L)*(E-B)]/V + [(K-L)*(B*A)]/V - I
the entire expression (S*(E-B))/V - [S*(F*A)]/V - [(K-L)*(E-B)]/V + [(K-L)*(B*A)]/V - I does not involve R, so we can call it X:
W*R = [(S*U) - (K-L)*U]*R/V + X
and letting Y = [(S*U) - (K-L)*U]/V we have:
W*R = Y*R + X, so
(W-Y)*R = X and
R = X/(W-Y) (assuming that W-Y is non-zero, which has to be checked separately).
the back-substitution is going to get REALLY messy, and i doubt there will be much cancellation.
If you group Letters and do some simple algebra:
k1R = k2R + K3
EDIT: Actually same reasoning applies if letters are matrices, assuming all operations are defined