Question 996404
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Find the sum of all solutions to e^{x^2}={e^{13x}}*{1/{e^{40}}}.
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You are given


{{{e^(x^2)}}} = {{{e^(13x)}}} . {{{1/e^40}}}.


It is the same as


{{{e^(x^2)}}} = {{{e^(13x-40)}}}.


The last equality implies that


{{{x^2}}} = {{{13x - 40}}}.


Rewrite this quadratic equation as


{{{x^2 - 13x + 40}}} = {{{0}}}.


You can find its solution using quadratic formula,  or applying the Viete's theorem,  or by factoring. 


In any case,  the roots of this quadratic equation are  {{{x[1]}}} = {{{5}}},   {{{x[2]}}} = {{{8}}}. 


The sum of the roots is  13.