document.write( "Question 206892: Remove radical and simplify..\r
\n" ); document.write( "\n" ); document.write( "radical of x-3 plus radical of 2x equals three? \n" ); document.write( "
Algebra.Com's Answer #156386 by Edwin McCravy(20054)\"\" \"About 
You can put this solution on YOUR website!
Remove radical and simplify..
\n" ); document.write( "radical of x-3 plus radical of 2x equals three?
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document.write( "\"sqrt%28x-3%29%2Bsqrt%282x%29=3\"\r\n" );
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document.write( "Isolate the more complicaed radical term.  So we\r\n" );
document.write( "isolate \"sqrt%28x-3%29\"\r\n" );
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document.write( "\"sqrt%28x-3%29=3-sqrt%282x%29\"\r\n" );
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document.write( "Square both sides:\r\n" );
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document.write( "\"%28sqrt%28x-3%29%29%5E2=%283-sqrt%282x%29%29%5E2\"\r\n" );
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document.write( "Write the square on the right as the product\r\n" );
document.write( "of the binomial with itself:\r\n" );
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document.write( "\"x-3=%283-sqrt%282x%29%29%283-sqrt%282x%29%29+\"\r\n" );
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document.write( "Use FOIL on the right sides:\r\n" );
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document.write( "\"x-3=9-3sqrt%282x%29-3sqrt%282x%29%2B%28sqrt%282x%29%29%5E2+\"\r\n" );
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document.write( "\"x-3=9-6sqrt%282x%29%2B+2x\"\r\n" );
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document.write( "Isolate the radical term:\r\n" );
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document.write( "\"6sqrt%282x%29=12%2Bx\"\r\n" );
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document.write( "Square both sides:\r\n" );
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document.write( "\"6sqrt%282x%29%29%5E2=%2812%2Bx%29%5E2\"\r\n" );
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document.write( "\"6%5E2%2A%28sqrt%282x%29%29%5E2=%2812%2Bx%29%2812%2Bx%29\"\r\n" );
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document.write( "\"36%282x%29=144%2B12x%2B12x%2Bx%5E2\"\r\n" );
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document.write( "\"72x=144%2B24x%2Bx%5E2\"\r\n" );
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document.write( "Get 0 on the left:\r\n" );
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document.write( "\"0=x%5E2-48x%2B144\"\r\n" );
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document.write( "That doesn't factor, so we have\r\n" );
document.write( "to use the quadratic formula:\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( "\"a=1\", \"b=-48\",  \"c=144\"\r\n" );
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document.write( "  \r\n" );
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document.write( " \"x+=+%2848+%2B-+sqrt%28+2304-576+%29%29%2F2+\" \r\n" );
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document.write( " \"x+=+%2848+%2B-+sqrt%281728%29%29%2F2+\"\r\n" );
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document.write( " \"x+=+%2848+%2B-+sqrt%28576%2A3%29%29%2F2+\"\r\n" );
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document.write( " \"x+=+%2848+%2B-+sqrt%28576%29sqrt%283%29%29%2F2+\"\r\n" );
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document.write( " \"x+=+%2848+%2B-+24sqrt%283%29%29%2F2+\"\r\n" );
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document.write( "Make two fractions:\r\n" );
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document.write( "\"x+=+48%2F2+%2B-+24sqrt%283%29%2F2+\"\r\n" );
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document.write( "\"x+=+24+%2B-+12sqrt%283%29+\"\r\n" );
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document.write( "Those have decimal values\r\n" );
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document.write( "\"x=24%2B12sqrt%283%29=44.78460969\"\r\n" );
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document.write( "\"x=24-12sqrt%283%29=3.215390309\"\r\n" );
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document.write( "Check these in the original with a\r\n" );
document.write( "calculator.  The first one doesn't\r\n" );
document.write( "check but the second one does.\r\n" );
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document.write( "So the only solution is\r\n" );
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document.write( "\"x=24-12sqrt%283%29=3.215390309\"\r\n" );
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document.write( "Edwin
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