document.write( "Question 687807: $\"sqrt%285-x%29=5-x%5E2\"$ \n" ); document.write( "

Algebra.Com's Answer #425361 by KMST(5347) $\"\"$ $\"About$

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If your problem was $\"sqrt%285-x%29=5-x%5E2\"$ ,
\n" ); document.write( "the first step to solve it would be squaring both sides of the equal sign.
\n" ); document.write( "That may introduce some extraneous solutions, but we can check the solutions and eliminate the ones that do not work.
\n" ); document.write( " $\"sqrt%285-x%29=5-x%5E2\"$ --> $\"5-x=%285-x%5E2%29%5E2\"$ <--> $\"5-x=25-10x%5E2%2Bx%5E4\"$ <--> $\"highlight%28x%5E4-10x%5E2%2Bx-20=0%29\"$
\n" ); document.write( "My problem at this point is that I cannot find exact solutions.
\n" ); document.write( "By graphing, or by smart guess and check, I can find as approximate solutions
\n" ); document.write( "-2.7913, -1.562, 1.791, and 2.562.
\n" ); document.write( "However, -2.7913, and 2.562 make $\"5-x%5E2\"$ negative,
\n" ); document.write( "so they are not solutions of the original $\"sqrt%285-x%29=5-x%5E2\"$ equation.
\n" ); document.write( "We are left with -1.562, and 1.791 as approximate solutions \n" ); document.write( "

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