document.write( "Question 298755: √x+6 + √2-x = 4 \n" ); document.write( "
Algebra.Com's Answer #214812 by Edwin McCravy(20054)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "\"sqrt%28x%2B6%29%2Bsqrt%282-x%29=4\"\r\n" );
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document.write( "Pick one of the radicals and label it R.\r\n" );
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document.write( "If we pick the first radical to label R then we have\r\n" );
document.write( "\"R=sqrt%28x%2B6%29=R\".  So substituting R for the first\r\n" );
document.write( "radical:\r\n" );
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document.write( "\"R%2Bsqrt%282-x%29=4\"\r\n" );
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document.write( "Isolate the radical term by subtracting R from both sides::\r\n" );
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document.write( "\"sqrt%282-x%29=4-R\"\r\n" );
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document.write( "Square both sides:\r\n" );
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document.write( "\"%28sqrt%282-x%29%29%5E2=%284-R%29%5E2\"\r\n" );
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document.write( "\"2-x=%284-R%29%284-R%29\"\r\n" );
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document.write( "FOIL out the right sides:\r\n" );
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document.write( "\"2-x=16-4R-4R%2BR%5E2\"\r\n" );
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document.write( "\"2-x=16-8R%2BR%5E2\"\r\n" );
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document.write( "Substitute \"sqrt%28x%2B6%29\" for R\r\n" );
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document.write( "\"2-x=16-8sqrt%28x%2B6%29%2B%28sqrt%28x%2B6%29%29%5E2\"\r\n" );
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document.write( "\"2-x=16-8sqrt%28x%2B6%29%2Bx%2B6\"\r\n" );
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document.write( "Isolate the radical term and simplify the above:\r\n" );
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document.write( "\"8sqrt%28x%2B6%29=20%2B2x\"\r\n" );
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document.write( "To make things easier divide every term by 2\r\n" );
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document.write( "\"4sqrt%28x%2B6%29=10%2Bx\"\r\n" );
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document.write( "Square both sides:\r\n" );
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document.write( "\"%284sqrt%28x%2B6%29%29%5E2=%2810%2Bx%29%5E2\"\r\n" );
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document.write( "\"4%5E2%2A%28sqrt%28x%2B6%29%29%5E2=%2810%2Bx%29%2810%2Bx%29\"\r\n" );
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document.write( "\"16%28x%2B6%29=100%2B10x%2B10x%2Bx%5E2\"\r\n" );
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document.write( "\"16x%2B96=100%2B20x%2Bx%5E2\"\r\n" );
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document.write( "Get 0 on the left side:\r\n" );
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document.write( "\"0=x%5E2%2B4x%2B4\"\r\n" );
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document.write( "\"0=%28x%2B2%29%28x%2B2%29\"\r\n" );
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document.write( "\"0=%28x%2B2%29%5E2\"\r\n" );
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document.write( "\"x%2B2%29=0\"\r\n" );
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document.write( "\"x=-2\"\r\n" );
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document.write( "But we must ALWAYS check equations with even root\r\n" );
document.write( "radicals as we often get extraneous solutions:\r\n" );
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document.write( "Checking:\r\n" );
document.write( "\"sqrt%28x%2B6%29%2Bsqrt%282-x%29=4\"\r\n" );
document.write( "\"sqrt%28%28-2%29%2B6%29%2Bsqrt%282-%28-2%29%29=4\"\r\n" );
document.write( "\"sqrt%284%29%2Bsqrt%282%2B2%29=4\"\r\n" );
document.write( "\"2%2Bsqrt%284%29=4\"\r\n" );
document.write( "\"2%2B2=4\"\r\n" );
document.write( "\"4=4\"\r\n" );
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document.write( "It checks, so the solution is \"x=-2\" \r\n" );
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document.write( "Edwin<
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