document.write( "Question 896466: Solve the following inequality showing your work: |X|=6-X^2 \n" ); document.write( "
Algebra.Com's Answer #543535 by Edwin McCravy(20081)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "  \"abs%28X%29=6-X%5E2\"\r\n" );
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document.write( "We square both sides:\r\n" );
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document.write( "  \"X%5E2=%286-X%5E2%29%5E2\"\r\n" );
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document.write( "  \"X%5E2=36-12X%5E2%2BX%5E4\"\r\n" );
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document.write( "  \"0=X%5E4-13X%5E2%2B36\"\r\n" );
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document.write( "  \"0=%28X%5E2-9%29%28X%5E2-4%29\"\r\n" );
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document.write( "  \"0=%28X-3%29%28X%2B3%29%28x-2%29%28X%2B2%29\"\r\n" );
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document.write( "We get 3, -3, 2, -2\r\n" );
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document.write( "But we must check for extraneous answers:\r\n" );
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document.write( "  \"abs%28X%29=6-X%5E2\" \r\n" );
document.write( "  \"abs%283%29=6-3%5E2\"\r\n" );
document.write( "  \"3=6-9\"\r\n" );
document.write( "  \"3=-3\"\r\n" );
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document.write( "3 is not a solution\r\n" );
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document.write( "  \"abs%28X%29=6-X%5E2\" \r\n" );
document.write( "  \"abs%28-3%29=6-%28-3%29%5E2\"\r\n" );
document.write( "  \"3=6-9\"\r\n" );
document.write( "  \"3=-3\"\r\n" );
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document.write( "-3 is not a solution\r\n" );
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document.write( "  \"abs%28X%29=6-X%5E2\" \r\n" );
document.write( "  \"abs%282%29=6-2%5E2\"\r\n" );
document.write( "  \"2=6-4\"\r\n" );
document.write( "  \"2=2\"\r\n" );
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document.write( "2 is a solution\r\n" );
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document.write( "  \"abs%28X%29=6-%28-2%29%5E2\" \r\n" );
document.write( "  \"abs%28-2%29=6-%28-2%29%5E2\"\r\n" );
document.write( "  \"2=6-4\"\r\n" );
document.write( "  \"2=2\"\r\n" );
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document.write( "-2 is a solution\r\n" );
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document.write( "So there are only two solutions, 2 and -2.\r\n" );
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document.write( "Edwin
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