# Solve not working

Posted 3 months ago
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 I am trying to solve the following equation for x, but it is not working at all. What I am doing wrong? c1 = 1.6*10^(-33) c2 = 5.23*10^(-27) eqn = ExpandAll[(c2/2) + ((1/c1)*(((x^2)/4) + c1)^(1/2)) == Log[(x/2 - ((((x^2)/4) + c1)^(1/2)))/((((x^2)/4) + c1 - x/2)^(1/2))]] Solve[eqn, x] 
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Posted 3 months ago
 You should add the domain Reals to Solve, i.e. Solve[eqn,x,Reals] Then Solve (as well as NSolve) ends quickly with the correct solution {}, i.e. there is no solution. Block[{c1, c2, x, eqn}, c1 = 1.6*10^(-33); c2 = 5.23*10^(-27); eqn = ExpandAll[(c2/2) + ((1/c1)*(((x^2)/4) + c1)^(1/2)) == Log[(x/2 - ((((x^2)/4) + c1)^(1/2)))/((((x^2)/4) + c1 - x/2)^(1/2))]]; Solve[eqn, x, Reals] ] {} You can see this when you take care of the legal real x-domains of the equations left and right side. From the Log-Expression on the right, one can see that: x/2 > Sqrt[c1 + x^2/4] must hold. But this is never True for non-negative c1.I have enhanced your code a bit. One can see there what happens. See the attachment. Set orgVals at will for your or my (somewhat nicer) c1-, c2-Values.BTW.: If you allow complex values, neither Solve nor DSolve can solve the problem. Attachments:
 Look at this c1 = 1.6*10^(-33); c2 = 5.23*10^(-27); Table[{x, (c2/2) + ((1/c1)*(((x^2)/4) + c1)^(1/2)), Log[(x/2 - ((((x^2)/4) + c1)^(1/2)))/((((x^2)/4) + c1 - x/2)^(1/2))]}, {x,-10,10}] which returns {{-10, 3.125*^33, 0.601986402162968 + Pi*I}, {-9, 2.8125*^33, 0.5928118328288697 + Pi*I}, {-8, 2.5*^33, 0.5815754049028404 + Pi*I}, {-7, 2.1875*^33, 0.5674899664194921 + Pi*I}, {-6, 1.875*^33, 0.549306144334055 + Pi*I}, {-5, 1.5625*^33, 0.5249110622493387 + Pi*I}, {-4, 1.25*^33, 0.49041462650586326 + Pi*I}, {-3, 9.375*^32, 0.43773436867694987 + Pi*I}, {-2, 6.25*^32, 0.3465735902799726 + Pi*I}, {-1, 3.125*^32, 0.1438410362258906 + Pi*I}, {0, 2.5*^16, 0. + Pi*I}, {1, 3.125*^32, Indeterminate}, {2, 6.25*^32, Indeterminate}, {3, 9.375*^32, Indeterminate}, {4, 1.25*^33, Indeterminate}, {5, 1.5625*^33, Indeterminate}, {6, 1.875*^33, Indeterminate}, {7, 2.1875*^33, Indeterminate}, {8, 2.5*^33, Indeterminate}, {9, 2.8125*^33, Indeterminate}, {10, 3.125*^33, Indeterminate}} along with warnings about a division by zero and 0.*ComplexInfinity