$$ \sqrt{x} + \sqrt{x - 20} = 10 $$
Is there a procedure other than guess and check that can be used to solve this?
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1Does this answer your question? General Principles of Solving Radical Equations. Or this, this, this, etc. – Jakob Streipel Sep 18 '22 at 15:18
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1We may notice that l.h.s. is a strictly increasing function of $x$. Hence there are no roots or there is only one root. We may notice that $x=36$ is a root, hence the answer is $36$. – Sergei Nikolaev Sep 18 '22 at 15:23
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I don't understand the answer in the general principles of solving radical equations but when I get more time I'll look more into it – Matthew S. Sep 18 '22 at 15:38