document.write( "Question 460650: this is from the 10th edition of the beginning algebra book. There are no instructions other than to solve. \r
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Algebra.Com's Answer #315983 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Let u = one of the radical terms, say\r\n" );
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document.write( "\"u=sqrt%28x%2B2%29\"\r\n" );
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document.write( "\"+sqrt%283x%2B3%29%2Bu=5+\"\r\n" );
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document.write( "Isolate the radical term:\r\n" );
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document.write( "\"+sqrt%283x%2B3%29=5-u\"\r\n" );
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document.write( "Square both sides:\r\n" );
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document.write( "\"3x%2B3+=+25-10u%2Bu%5E2\"\r\n" );
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document.write( "Replace u by \"sqrt%28x%2B2%29\" and u² by x+2\r\n" );
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document.write( "\"3x%2B3+=+25-10sqrt%28x%2B2%29%2Bx%2B2\"\r\n" );
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document.write( "\"3x%2B3+=+27-10sqrt%28x%2B2%29%2Bx\"\r\n" );
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document.write( "Isolate the radical term:\r\n" );
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document.write( "\"10sqrt%28x%2B2%29=24-2x\"\r\n" );
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document.write( "Divide every term by 2 since they are all even:\r\n" );
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document.write( "\"5sqrt%28x%2B2%29=12-x\"\r\n" );
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document.write( "Square both sides:\r\n" );
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document.write( "\"25%28x%2B2%29+=+144-24x%2Bx%5E2\"\r\n" );
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document.write( "25x + 50 = 144 - 24x + x²\r\n" );
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document.write( "Get 0 on the left side:\r\n" );
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document.write( "0 = x² - 49x + 94\r\n" );
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document.write( "Factor the right side:\r\n" );
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document.write( "0 = (x - 2)(x - 47}\r\n" );
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document.write( "Use the zero factor principle\r\n" );
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document.write( "x - 2 = 0        x - 47 = 0\r\n" );
document.write( "    x = 2             x = 47\r\n" );
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document.write( "But we must always check a radical equation,\r\n" );
document.write( "because sometimes there may be a \"phony\"\r\n" );
document.write( "solution, called \"extraneous\".  \r\n" );
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document.write( "Checking x = 2\r\n" );
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document.write( "\"+sqrt%283x%2B3%29%2Bsqrt%28x%2B2%29=5+\"\r\n" );
document.write( "\"+sqrt%283%282%29%2B3%29%2Bsqrt%282%2B2%29=5+\"\r\n" );
document.write( "\"+sqrt%286%2B3%29%2Bsqrt%282%2B2%29=5+\"\r\n" );
document.write( "\"+sqrt%289%29%2Bsqrt%284%29=5+\"\r\n" );
document.write( "\"3%2B2=5\"\r\n" );
document.write( "\"5=5\"\r\n" );
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document.write( "That checks so x = 2 is a solution.\r\n" );
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document.write( "Checking x = 47\r\n" );
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document.write( "\"+sqrt%283%2847%29%2B3%29%2Bsqrt%2847%2B2%29=5+\"\r\n" );
document.write( "\"+sqrt%28141%2B3%29%2Bsqrt%2849%29=5+\"\r\n" );
document.write( "\"+sqrt%28144%29%2B7=5+\"\r\n" );
document.write( "\"12%2B7=5\"\r\n" );
document.write( "\"19=5\"\r\n" );
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document.write( "That is false so x = 47 is a \"phony\"\r\n" );
document.write( "or \"irrational\" solution.  So the\r\n" );
document.write( "only solution is x = 2\r\n" );
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document.write( "Edwin
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