document.write( "Question 640044: Solve: √x-6 + √x = 6 (x-6 is all under the square root) \n" ); document.write( "

Algebra.Com's Answer #403004 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "Öx - 6 + Öx = 6\r\n" );
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document.write( "Isolate the more complicated radical term:\r\n" );
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document.write( "     Öx - 6 = 6 - Öx\r\n" );
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document.write( "Square both sides:\r\n" );
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document.write( "  (Öx - 6)² = (6 - Öx)²\r\n" );
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document.write( "      x - 6 = (6 - Öx)(6 - Öx)\r\n" );
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document.write( "      x - 6 = 36 - 6Öx - 6Öx + x\r\n" );
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document.write( "      x - 6 = 36 - 12Öx + x\r\n" );
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document.write( "Isolate the radical term on the right\r\n" );
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document.write( "              42 = 12Öx\r\n" );
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document.write( "Divide both sides by 6\r\n" );
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document.write( "               7 = 2Öx\r\n" );
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document.write( "Square both sides:\r\n" );
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document.write( "              7² = (2Öx)²\r\n" );
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document.write( "              49 = 4x\r\n" );
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document.write( "               = x\r\n" );
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document.write( "You must check all radical equation because sometimes\r\n" );
document.write( "squaring both sides often introduces extraneous \"solutions\".  \r\n" );
document.write( "It'll be easier to check if we convert  to a decimal 12.25\r\n" );
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document.write( "               Öx - 6 + Öx = 6\r\n" );
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document.write( "       Ö12.25 - 6 + Ö12.25 = 6\r\n" );
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document.write( "          Ö6.25 + Ö12.25 = 6\r\n" );
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document.write( "               2.5 + 3.5 = 6\r\n" );
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document.write( "                       6 = 6                                \r\n" );
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document.write( "So the solution is  or 12.25\r\n" );
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document.write( "Edwin

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