document.write( "Question 70150This question is from textbook College Algebra Essentials
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Algebra.Com's Answer #50012 by Edwin McCravy(20054)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "\"2x+-+3x%5E%281%2F2%29+%2B+1+=+0\"\r\n" );
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document.write( "Two ways to solve it. Pick whichever one\r\n" );
document.write( "is the method you are studying now.\r\n" );
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document.write( "Method 1.\r\n" );
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document.write( "Change \"x%5E%281%2F2%29\" to \"sqrt%28x%29\"\r\n" );
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document.write( "\"2x+-+3sqrt%28x%29+%2B+1+=+0\"\r\n" );
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document.write( "Isolate the radical term\r\n" );
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document.write( "\"2x+%2B+1+=+3sqrt%28x%29\"\r\n" );
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document.write( "Square both sides of the equation:\r\n" );
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document.write( "\"%282x+%2B+1%29%5E2+=+%283sqrt%28x%29%29%5E2\"\r\n" );
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document.write( "\"%282x+%2B+1%29%282x+%2B+1%29+=+9x+\"\r\n" );
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document.write( "\"4x%5E2%2B2x%2B2x%2B1+=+9x+\"\r\n" );
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document.write( "\"4x%5E2%2B4x%2B1+=+9x\"\r\n" );
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document.write( "Get 0 on the right by subtracting 9x \r\n" );
document.write( "from both sides:\r\n" );
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document.write( "\"4x%5E2-5x%2B1=0\"\r\n" );
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document.write( "Factor the left side\r\n" );
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document.write( "\"%284x-1%29%28x-1%29=0\"\r\n" );
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document.write( "Setting \"4x-1=0\" gives \"x=1%2F4\"\r\n" );
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document.write( "Setting \"x-1=0\" gives \"x=1\"\r\n" );
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document.write( "Both answers check.\r\n" );
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document.write( "Method 2.\r\n" );
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document.write( "\"2x+-+3x%5E%281%2F2%29+%2B+1+=+0\"\r\n" );
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document.write( "Let \"x%5E%281%2F2%29+=+w\"\r\n" );
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document.write( "Then squaring both sides of that we have\r\n" );
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document.write( "   \"x+=+w%5E2\"\r\n" );
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document.write( "So the equation becomes\r\n" );
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document.write( "\"2w%5E2+-+3w+%2B+1+=+0\"\r\n" );
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document.write( "Now we factor the left side:\r\n" );
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document.write( "\"%282w-1%29%28w-1%29=0\"\r\n" );
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document.write( "\"2w-1=0\" gives \"w=1%2F2\"\r\n" );
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document.write( "\"w-1=0\" gives \"x=1\"\r\n" );
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document.write( "But we want x, not w, so since\r\n" );
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document.write( "\"x+=+w%5E2\"\r\n" );
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document.write( "For \"w=1%2F2\"\r\n" );
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document.write( "\"x+=+w%5E2+=+%281%2F2%29%5E2+=+1%2F4\"  \r\n" );
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document.write( "For \"w=1\"\r\n" );
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document.write( "\"x+=+w%5E2+=+1%5E2+=+1\"  \r\n" );
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document.write( "Edwin
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