document.write( "Question 987319: Solve the equation sqrt(8x) + sqrt(2x)- sqrt(x/8) =110.  \n" ); document.write( "
Algebra.Com's Answer #608090 by ikleyn(52787)\"\" \"About 
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\n" ); document.write( "Your equation is\r
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\n" ); document.write( "\n" ); document.write( "\"sqrt%288x%29\" + \"sqrt%282x%29\"- \"sqrt%28x%2F8%29\" = \"110\". \r
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\n" ); document.write( "\n" ); document.write( "Notice that \r
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\n" ); document.write( "\n" ); document.write( "\"sqrt%288x%29\" = \"sqrt%288%29\"\"sqrt%28x%29\" = \"2sqrt%282%29\"\"sqrt%28x%29\",\r
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\n" ); document.write( "\n" ); document.write( "\"sqrt%282x%29\" = \"sqrt%282%29\"\"sqrt%28x%29\",     and \r
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\n" ); document.write( "\n" ); document.write( "\"sqrt%28x%2F8%29\" = \"sqrt%281%2F8%29\"\"sqrt%28x%29\" = \"1%2F%282sqrt%282%29%29\"\"sqrt%28x%29\" = \"sqrt%282%29%2F%282%2A2%29\"\"sqrt%28x%29\" = \"sqrt%282%29%2F4\"\"sqrt%28x%29\". \r
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\n" ); document.write( "\n" ); document.write( "Hence,  your equations takes the form\r
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\n" ); document.write( "\n" ); document.write( "\"2sqrt%282%29\"\"sqrt%28x%29\" + \"sqrt%282%29\"\"sqrt%28x%29\" - \"sqrt%282%29%2F4\"\"sqrt%28x%29\" = 110,     or \r
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\n" ); document.write( "\n" ); document.write( "\"%282sqrt%282%29+%2B+sqrt%282%29+-+sqrt%282%29%2F4%29\"\"sqrt%28x%29\" = 110,\r
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\n" ); document.write( "\n" ); document.write( "Now,  multiply both sides by  4  and then collect the common terms:\r
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\n" ); document.write( "\n" ); document.write( "\"%288sqrt%282%29+%2B+4sqrt%282%29+-+sqrt%282%29%29\"\"sqrt%28x%29\" = 440,\r
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\n" ); document.write( "\n" ); document.write( "\"11sqrt%282%29\"\"sqrt%28x%29\" = 440.\r
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\n" ); document.write( "\n" ); document.write( "Hence, \r
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\n" ); document.write( "\n" ); document.write( "\"sqrt%28x%29\" = \"440%2F%2811sqrt%282%29%29\" = \"40%2Fsqrt%282%29\" = \"%2840%2Asqrt%282%29%29%2F2\" = \"20sqrt%282%29\".\r
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\n" ); document.write( "\n" ); document.write( "Therefore,  x = 400*2 = 800.\r
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\n" ); document.write( "\n" ); document.write( "Answer.  x = 800.\r
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