document.write( "Question 172238This question is from textbook Introductory Algebra
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Algebra.Com's Answer #127289 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
Solve \r
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document.write( "Isolate the radical term by subtracting \"x%5E2\" from both sides:\r\n" );
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document.write( "\"sqrt%2822x%29+=+-x%5E2\"\r\n" );
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document.write( "Square both sides:\r\n" );
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document.write( "\"%28sqrt%2822x%29%29%5E2=%28-x%5E2%29%5E2\"\r\n" );
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document.write( "\"22x=x%5E4\"\r\n" );
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document.write( "\"22x-x%5E4=0\"\r\n" );
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document.write( "\"x%2822-x%5E3%29=0\"\r\n" );
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document.write( "We must always check even-root radical equations,\r\n" );
document.write( "because there may be extraneous solutions,\r\n" );
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document.write( "Checking \"x=0\"\r\n" );
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document.write( "\"x%5E2+%2B+sqrt%2822x%29+=+0\"\r\n" );
document.write( "\"0%5E2+%2B+sqrt%2822%280%29%29+=+0\"\r\n" );
document.write( "\"0+%2B+sqrt%280%29+=+0\"\r\n" );
document.write( "\"0+%2B+0+=+0\"\r\n" );
document.write( "\"0=0\"\r\n" );
document.write( "root(3,22)\r\n" );
document.write( "Checking \"x=root%283%2C22%29\"\r\n" );
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document.write( "\"x%5E2+%2B+sqrt%2822x%29+=+0\"\r\n" );
document.write( "\"%28root%283%2C22%29%29%5E2+%2B+sqrt%2822root%283%2C22%29%29+=+0\"\r\n" );
document.write( "\"22%5E%282%2F3%29+%2B+sqrt%2822%5E1%2A22%5E%281%2F3%29%29=0\"\r\n" );
document.write( "\"22%5E%282%2F3%29+%2B+sqrt%2822%5E%281%2B1%2F3%29%29=0\"\r\n" );
document.write( "\"22%5E%282%2F3%29+%2B+sqrt%2822%5E%283%2F3%2B1%2F3%29%29=0\"\r\n" );
document.write( "\"22%5E%282%2F3%29+%2B+sqrt%2822%5E%284%2F3%29%29=0\"\r\n" );
document.write( "\"22%5E%282%2F3%29+%2B+%2822%5E%284%2F3%29%29%5E%281%2F2%29=0\"\r\n" );
document.write( "\"22%5E%282%2F3%29+%2B+22%5E%28%284%2F3%29%281%2F2%29%29=0\"\r\n" );
document.write( "\"22%5E%282%2F3%29+%2B+22%5E%282%2F3%29=0\"\r\n" );
document.write( "\"2%2A22%5E%282%2F3%29=0\"\r\n" );
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document.write( "That is false so \"x=root%283%2C22%29\" is not a\r\n" );
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document.write( "So \"x=0\" is the only solution.\r\n" );
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document.write( "Here is how we could have solved this much easier:\r\n" );
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document.write( "\"x%5E2+%2B+sqrt%2822x%29+=+0\"\r\n" );
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document.write( "Isolate the radical term by subtracting \"x%5E2\" from both sides:\r\n" );
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document.write( "\"sqrt%2822x%29+=+-x%5E2\"\r\n" );
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document.write( "A square root radical always represents a non-negative number,\r\n" );
document.write( "so the left side is non-negative.  The right side, however, will\r\n" );
document.write( "always be negative unless \"x=0\".  So 0 is the only possible\r\n" );
document.write( "solution, and we check it as above and find it is a solution,\r\n" );
document.write( "so the only solution is \"x=0\".\r\n" );
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document.write( "Edwin
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