document.write( "Question 282020: square root of 4x+5-square root of 3x-6=8 \n" ); document.write( "
Algebra.Com's Answer #204827 by Edwin McCravy(20060)\"\" \"About 
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document.write( "\"sqrt%284x%2B5%29-sqrt%283x-6%29=8\"\r\n" );
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document.write( "Let \"A=sqrt%284x%2B5%29\" and \"B=sqrt%283x-6%29\"\r\n" );
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document.write( "\"A-B=8\"\r\n" );
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document.write( "Solve for one of the letters, say A:\r\n" );
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document.write( "\"A=8%2BB\"\r\n" );
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document.write( "Square both sides:\r\n" );
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document.write( "\"A%5E2=%288%2BB%29%5E2\"\r\n" );
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document.write( "\"A%5E2=64%2B16B%2BB%5E2\"\r\n" );
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document.write( "Replace \"A%5E2\" by \"A=4x%2B5\" and \"B%5E2\" by \"3x-6\"\r\n" );
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document.write( "\"4x%2B5=64%2B16B%2B3x-6\"\r\n" );
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document.write( "Solve for 16B:\r\n" );
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document.write( "\"4x%2B5=58%2B16B%2B3x\"\r\n" );
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document.write( "\"x%2B5=58%2B16B\"\r\n" );
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document.write( "\"x-53=16B\"\r\n" );
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document.write( "Square both sides:\r\n" );
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document.write( "\"x%5E2-106x%2B2809=256B%5E2\"\r\n" );
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document.write( "Replace \"B%5E2\" by \"3x-6\"\r\n" );
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document.write( "\"x%5E2-106x%2B2809=256%283x-6%29\"\r\n" );
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document.write( "\"x%5E2-106x%2B2809=768x-1536\"\r\n" );
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document.write( "\"x%5E2-874x%2B4345=0\"\r\n" );
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document.write( "Factor the left side:\r\n" );
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document.write( "\"%28x-869%29%28x-5%29=0\"\r\n" );
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document.write( "Solutions are \"x=869\" and \"x=5\"\r\n" );
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document.write( "We must check even root radical equations for extraneous solutions:\r\n" );
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document.write( "Substitute \"x=869\" into original equation:\r\n" );
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document.write( "\"sqrt%284x%2B5%29-sqrt%283x-6%29=8\"\r\n" );
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document.write( "\"sqrt%284%28869%29%2B5%29-sqrt%283%28869%29-6%29=8\"\r\n" );
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document.write( "\"sqrt%283481%29-sqrt%282601%29=8\"\r\n" );
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document.write( "\"59-51=8\"\r\n" );
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document.write( "\"8=8\"\r\n" );
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document.write( "That is true so \"x=869\" is a solution to the\r\n" );
document.write( "original equation.\r\n" );
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document.write( "Substitute \"x=5\" into original equation:\r\n" );
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document.write( "\"sqrt%284x%2B5%29-sqrt%283x-6%29=8\"\r\n" );
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document.write( "\"sqrt%284%285%29%2B5%29-sqrt%283%285%29-6%29=8\"\r\n" );
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document.write( "\"sqrt%2825%29-sqrt%289%29=8\"\r\n" );
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document.write( "\"5-3=8\"\r\n" );
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document.write( "\"2=8\"\r\n" );
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document.write( "That is false so \"x=5\" is not a solution to the\r\n" );
document.write( "original equation.\r\n" );
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document.write( "So there is one solution \"x=869\"\r\n" );
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document.write( "Edwin

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