document.write( "Question 829491: Please help me solve this equation: sqrt(9x-5)=3x^2+2x+3 \n" ); document.write( "
Algebra.Com's Answer #499892 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "\"sqrt%289x-5%29\"\"%22%22=%22%22\"\"3x%5E2%2B2x%2B3\"\r\n" );
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document.write( "Square both sides:\r\n" );
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document.write( "\"%28sqrt%289x-5%29%29%5E2\"\"%22%22=%22%22\"\"%283x%5E2%2B2x%2B3%29%5E2\"\r\n" );
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document.write( "\"9x-5\"\"%22%22=%22%22\"\"9x%5E4%2B4x%5E2%2B9%2B12x%5E3%2B18x%5E2%2B12x\"\r\n" );
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document.write( "\"9x-5\"\"%22%22=%22%22\"\"9x%5E4%2B22x%5E2%2B9%2B12x%5E3%2B12x\"\r\n" );
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document.write( "   \"%220%22\"\"%22%22=%22%22\"\"9x%5E4%2B22x%5E2%2B14%2B12x%5E3%2B3x\"\r\n" );
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document.write( "   \"%220%22\"\"%22%22=%22%22\"\"9x%5E4%2B12x%5E3%2B22x%5E2%2B3x%2B14\"\r\n" );
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document.write( "There are no sign changes, so by Descartes' rule of signs,\r\n" );
document.write( "there are no positive roots.\r\n" );
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document.write( "However any non-positive value of x would cause the left\r\n" );
document.write( "side of the equation\r\n" );
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document.write( "\"sqrt%289x-5%29\"\"%22%22=%22%22\"\"3x%5E2%2B2x%2B3\"\r\n" );
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document.write( "to be the square root of a negative number, which is not a real \r\n" );
document.write( "number.\r\n" );
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document.write( "Therefore there are no real solutions.\r\n" );
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document.write( "Edwin
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