Question 687807
If your problem was {{{sqrt(5-x)=5-x^2}}},
the first step to solve it would be squaring both sides of the equal sign.
That may introduce some extraneous solutions, but we can check the solutions and eliminate the ones that do not work.
{{{sqrt(5-x)=5-x^2}}} --> {{{5-x=(5-x^2)^2}}} <--> {{{5-x=25-10x^2+x^4}}} <--> {{{highlight(x^4-10x^2+x-20=0)}}}
My problem at this point is that I cannot find exact solutions.
By graphing, or by smart guess and check, I can find as approximate solutions
-2.7913, -1.562, 1.791, and 2.562.
However, -2.7913, and 2.562 make {{{5-x^2}}} negative,
so they are not solutions of the original {{{sqrt(5-x)=5-x^2}}} equation.
We are left with -1.562, and 1.791 as approximate solutions