document.write( "Question 707774: step by step solution to
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Algebra.Com's Answer #435852 by Edwin Parker(36)\"\" \"About 
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document.write( "    √3x+4 - √2x+4 = 2\r\n" );
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document.write( "Isolate either one of the radicals.\r\n" );
document.write( "I'll isolate the first radical on the left side:\r\n" );
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document.write( "            √3x+4 = 2 + √2x+4\r\n" );
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document.write( "Square both sides:\r\n" );
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document.write( "         (√3x+4)² = (2 + √2x+4)²\r\n" );
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document.write( "             3x+4 = (2 + √2x+4)(2 + √2x+4)\r\n" );
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document.write( "FOIL out the right side\r\n" );
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document.write( "             3x+4 = 4 + 2√2x+4 + 2√2x+4 + 2x+4\r\n" );
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document.write( "             3x+4 = 4 + 4√2x+4 + 2x+4\r\n" );
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document.write( "             3x+4 = 8 + 4√2x+4 + 2x\r\n" );
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document.write( "Isolate the remaining radical term on the right:\r\n" );
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document.write( "              x-4 = 4√2x+4\r\n" );
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document.write( "Square both sides:\r\n" );
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document.write( "           (x-4)² = (4√2x+4)²\r\n" );
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document.write( "       (x-4)(x-4) = 16(2x+4)\r\n" );
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document.write( "         x²-8x+16 = 32x+64\r\n" );
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document.write( "        x²-40x-48 = 0\r\n" );
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document.write( "That doesn't factor so we have 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( "                x = \"%28-%28-40%29+%2B-+sqrt%28+%28-40%29%5E2-4%2A%281%29%2A%28-48%29+%29%29%2F%282%2A%281%29%29+\" \r\n" );
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document.write( "                x = \"%2840+%2B-+sqrt%281600%2B192+%29%29%2F2+\"  \r\n" );
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document.write( "                x = \"%2840+%2B-+sqrt%281792+%29%29%2F2+\"\r\n" );
document.write( "     \r\n" );
document.write( "                x = \"%2840+%2B-+sqrt%28256%2A7+%29%29%2F2+\"\r\n" );
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document.write( "                x = \"%2840+%2B-+16sqrt%287%29%29%2F2+\"\r\n" );
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document.write( "                x = \"%288%285+%2B-+2sqrt%287%29%29%29%2F2+\"\r\n" );
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document.write( "                x = 4(5 ± 2√7)\r\n" );
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document.write( "Using the +,    x = 4(5 + 2√7), approximately 41.16601049\r\n" );
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document.write( "Using the -,    x = 4(5 - 2√7), approximately -1.166010489\r\n" );
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document.write( "We must check for extraneous solutions:\r\n" );
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document.write( "    √3x+4 - √2x+4 = 2\r\n" );
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document.write( "Checking 41.2  (rounded to tenths)\r\n" );
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document.write( "√3(41.2)+4 - √2(41.2)+4 = 2\r\n" );
document.write( "√127.6 - √86.4 = 2\r\n" );
document.write( "11.296 - 9.295 = 2\r\n" );
document.write( "         2.001 = 2\r\n" );
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document.write( "Not a perfect check, but close enough to believe it's \r\n" );
document.write( "a solution, sibce we rounded off.\r\n" );
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document.write( "x = 4(5 + 2√7), \r\n" );
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document.write( "Checking -1.17  (rounded to hundredths)\r\n" );
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document.write( "√3(-1.17)+4 - √2(-1.17)+4 = 2\r\n" );
document.write( "√2(41.2)+4 - √.49 = 2\r\n" );
document.write( "   .7 - 1.66 = 2\r\n" );
document.write( "        -.96 = 2\r\n" );
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document.write( "That's not close at all, so we believe it\r\n" );
document.write( "is extraneous, and not a solution.\r\n" );
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document.write( "So there is just one solution:  x = 4(5 + 2√7).\r\n" );
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document.write( "Edwin

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