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Notes for this derivation:
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Index  Inference Rule  Input latex  Feeds latex  Output latex  step validity  dimension check  unit check  notes 

10  subtract X from both sides 



LHS diff is 0 RHS diff is sqrt((pdg1939**2  4*pdg4231*pdg9139)/pdg9139**2) 
5982958249:
9582958293: 
5982958249:
9582958293: 

10.5  subtract X from both sides 



LHS diff is 0 RHS diff is sqrt((pdg1939**2  4*pdg4231*pdg9139)/pdg9139**2) 
9582958294:
5982958248: 
9582958294:
5982958248: 

11  simplify 



LHS diff is 0 RHS diff is (pdg9139*sqrt((pdg1939**2  4*pdg4231*pdg9139)/pdg9139**2) + sqrt(pdg1939**2  4*pdg4231*pdg9139))/(2*pdg9139) 
5982958248:
9999999968: 
5982958248:
9999999968: 

11.5  simplify 



LHS diff is 0 RHS diff is (pdg9139*sqrt((pdg1939**2  4*pdg4231*pdg9139)/pdg9139**2)  sqrt(pdg1939**2  4*pdg4231*pdg9139))/(2*pdg9139) 
9582958293:
9999999969: 
9582958293:
9999999969: 

5  add X to both sides 



valid 
5938459282:
5928292841: 
5938459282:
5928292841: 

4  subtract X from both sides 



LHS diff is pdg1464*(pdg1939 + pdg9139)/pdg9139 RHS diff is 0 
5958392859:
5938459282: 
5958392859:
5938459282: 

9  square root both sides 



no check performed 
9385938295:
5982958249: 9582958294: 
9385938295:
5982958249: 9582958294: 

8  LHS of expr 1 equals LHS of expr 2 



input diff is 0 diff is (pdg1464**2*pdg9139 + pdg1464*pdg1939 + pdg4231)/pdg9139 diff is (pdg1464**2*pdg9139 + pdg1464*pdg1939 + pdg4231)/pdg9139 
5928292841:
5959282914: 9385938295: 
5928292841:
5959282914: 9385938295: 

7  simplify 



valid 
5928285821:
5959282914: 
5928285821:
5959282914: 

6  change variable X to Y 



valid 
8582954722:
dimensions are consistent 5928285821: 
8582954722:
N/A 5928285821: 

14  declare final expr 



no validation is available for declarations 
9999999968:

9999999968:


15  declare final expr 



no validation is available for declarations 
9999999969:

9999999969:


3  divide both sides by 



LHS diff is pdg1464*(pdg1939  pdg9139)/pdg9139 RHS diff is 0 
9285928292:
5958392859: 
9285928292:
5958392859: 

1  declare initial expr 



no validation is available for declarations 
9285928292:

9285928292:


7.5  declare initial expr 



no validation is available for declarations 
8582954722:
dimensions are consistent 
8582954722:
N/A 
symbol ID  category  latex  scope  dimension  name  value  Used in derivations  references  

3410  variable 
h
\(h\) 
real 

none 

2  
4231  variable 
c
\(c\) 
['real'] 

12  
1464  variable 
x
\(x\) 
['real'] 


140  
1939  variable 
b
\(b\) 
['real'] 

20  
9139  variable 
a
\(a\) 
['real'] 

45 