document.write( "Question 5219: Find the real solution.\r
\n" ); document.write( "\n" ); document.write( "\"x%5E4-10x%5E2%2B25=0\"
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Algebra.Com's Answer #2686 by ichudov(507)\"\" \"About 
You can put this solution on YOUR website!
This is a typical school problem with fourth and second degree in a trinomial. They are all solved the same way. \r
\n" ); document.write( "\n" ); document.write( "Use y instead of \"x%5E2\". \"x%5E4\" is \"y%5E2\". \r
\n" ); document.write( "\n" ); document.write( "\"y%5E2-10y%2B25=0\"\r
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Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation \"ay%5E2%2Bby%2Bc=0\" (in our case \"1y%5E2%2B-10y%2B25+=+0\") has the following solutons:
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\n" ); document.write( " \"y%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"
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\n" ); document.write( " For these solutions to exist, the discriminant \"b%5E2-4ac\" should not be a negative number.
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\n" ); document.write( " First, we need to compute the discriminant \"b%5E2-4ac\": \"b%5E2-4ac=%28-10%29%5E2-4%2A1%2A25=0\".
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\n" ); document.write( " Discriminant d=0 is zero! That means that there is only one solution: \"y+=+%28-%28-10%29%29%2F2%5C1\".
\n" ); document.write( " Expression can be factored: \"1y%5E2%2B-10y%2B25+=+1%28y-5%29%2A%28y-5%29\"
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\n" ); document.write( " Again, the answer is: 5, 5.\n" ); document.write( "Here's your graph:
\n" ); document.write( "\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-10%2Ax%2B25+%29\"

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\n" ); document.write( "\n" ); document.write( "As you can see, the only solution is y=5, or \"x%5E2=5\". So, x is either \"sqrt%285%29\", or \"sqrt%28-5%29\"
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