[benworld128]

Original Problem

A + C -> D + E

A -> B + X   H1 = 25.6
D -> C + X   H2 = -526.30
D + E -> C + B  = H3 = -48.9

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How I solve the problem
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Flip H2 and Flip H3  so we get

A      ->  B + X
C + X ->  D
C + B -> D + E   
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Cross X out and B out so we get

A + 2C -> 2D +  E   

Now do I multiply by (1/2) ? I am lost ?

Any help ?

Thank you

[Sanger]

I believe that it is not solvable. 
H1 and H3 must have the same coefficient, as does H1 and H2.  You must reverse H3. H1 must stay as it is.  In order to eliminate the X's from both sides, however, H2 must be switched. 
This will just give you
 A + 2C -> 2D + E
Correct me if I am wrong, but there seems to be no other way to solve this.  The question must've contained a mistake.

[Borek]

That was my impression as well - no solution.