Question 1206468
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<pre>

Go to web-site

https://www.wolframalpha.com/widgets/gallery/view.jsp?id=b858339e64fa997454dd12f77cb1ece1


(wolfram alpha zeros calculator).


Print your expression for the function

    x + sqrt((x-0.5)+sqrt(x+0.25))-1024,

which represents  f(x) = {{{x + sqrt((x-0.5)+sqrt(x+0.25))-1024}}}


and click the "Submit" button.  So, you want to get an approximation solution to this equation f(x) = 0.


You will get the number x = 992.02,  which is really a good approximation to the solution.


<U>CHECK</U>.  f(992.02) = 1024.005...

        f(992)    = 1023.984...
</pre>


What I want to say at the end, is THIS: there is no Algebra method/methods 
for finding/searching exact solution/solutions to this equation.


There are numerical methods, instead, that provide approximate solution.