document.write( "Question 164961This question is from textbook Elementary and Intermediate
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Algebra.Com's Answer #121585 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Put parentheses around the first two terms:\r\n" );
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document.write( "\"%28x%5E2%2Bx%29%2B+sqrt%28x%5E2%2Bx%29-2=0\"\r\n" );
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document.write( "Notice that \"%28x%5E2%2Bx%29\" occurs in two places, so let the\r\n" );
document.write( "variable part of the middle term, in this case the whole\r\n" );
document.write( "middle term, \"sqrt%28x%5E2%2Bx%29\"be equal to the letter \"W\".\r\n" );
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document.write( "That is to say we are letting \r\n" );
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document.write( "\"sqrt%28x%5E2%2Bx%29+=+W\"\r\n" );
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document.write( "Now we square both sides:\r\n" );
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document.write( "\"%28sqrt%28x%5E2%2Bx%29%29%5E2+=+W%5E2\"\r\n" );
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document.write( "\"%28x%5E2%2Bx%29=+W%5E2\"\r\n" );
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document.write( "So we substitute \"W%5E2\" for \"%28x%5E2%2Bx%29\" in the original \r\n" );
document.write( "equation, and \"W\" for \"sqrt%28x%5E2%2Bx%29\"\r\n" );
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document.write( "\"%28x%5E2%2Bx%29%2B+sqrt%28x%5E2%2Bx%29-2=0\"\r\n" );
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document.write( "becomes the much simpler looking equation:\r\n" );
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document.write( "\"W%5E2%2BW-2=0\"\r\n" );
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document.write( "Factoring:\r\n" );
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document.write( "\"%28W%2B2%29%28W-1%29=0\"\r\n" );
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document.write( "Using the zero-factor property,\r\n" );
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document.write( "   \r\n" );
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document.write( "So now we have to substitute back.\r\n" );
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document.write( "\"W+=+sqrt%28x%5E2%2Bx%29\"\r\n" );
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document.write( "We can tell immediately that \"sqrt%28x%5E2%2Bx%29=-2\" has no\r\n" );
document.write( "solution because square roots when written as a radical\r\n" );
document.write( "are never negative, so that square root on the left\r\n" );
document.write( "could not equal to -2 on the right.\r\n" );
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document.write( "So we solve\r\n" );
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document.write( "\"sqrt%28x%5E2%2Bx%29=1\"\r\n" );
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document.write( "Square both sides:\r\n" );
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document.write( "\"%28sqrt%28x%5E2%2Bx%29%29%5E2=%281%29%5E2\" \r\n" );
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document.write( "\"x%5E2%2Bx=1\"\r\n" );
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document.write( "\"x%5E2%2Bx-1=0\"\r\n" );
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document.write( "\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"\r\n" );
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document.write( "\"x+=+%28-1+%2B-+sqrt%28+1%5E2-4%2A1%2A%28-1%29+%29%29%2F%282%2A1%29+\"\r\n" );
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document.write( "\"x+=+%28-1+%2B-+sqrt%28+1%2B4%29%29%2F%282%29+\"\r\n" );
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document.write( "\"x+=+%28-1+%2B-+sqrt%285%29%29%2F2+\"\r\n" );
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document.write( "Edwin

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