document.write( "Question 1055142: x^2 - 6x- (x^2 -6x - 3 )^1/2 =5 \n" ); document.write( "
Algebra.Com's Answer #670373 by Edwin McCravy(20055) $\"\"$ $\"About$
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document.write( "Since x²-6x appears twice, let u = x²-6x\r\n" );
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document.write( "Isolate the square root on the right side:\r\n" );
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document.write( "Square both sides\r\n" );
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document.write( "Get 0 on the right\r\n" );
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document.write( "Factor the left side:\r\n" );
document.write( "(u-4)(u-7) = 0\r\n" );
document.write( "u-4 = 0;  u = 7\r\n" );
document.write( "  u = 4;  u = 7\r\n" );
document.write( "Since u = x²-6x\r\n" );
document.write( "  x²-6x = 4;       x²-6x = 7\r\n" );
document.write( "x²-6x-4 = 0;     x²-6x-7 = 0\r\n" );
document.write( "              (x-7)(x+1) = 0\r\n" );
document.write( "               x-7 = 0; x+1 = 0\r\n" );
document.write( "                 x = 7;   x = -1\r\n" );
document.write( "Since x²-6x-4 does not factor \r\n" );
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document.write( "Four potential solutions.\r\n" );
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document.write( "7, -1, , \r\n" );
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document.write( "But we must check all solutions when there is a square\r\n" );
document.write( "root radical with a variable underneath contained in the \r\n" );
document.write( "original equation.\r\n" );
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document.write( "Checking x=7 in the original equation:\r\n" );
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document.write( "That checks, So x=7 IS a solution\r\n" );
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document.write( "Checking x=-1 in the original equation:\r\n" );
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document.write( "That checks, So x=-1 IS a solution\r\n" );
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document.write( "Checking x=3 + sqrt(13) in the original equation:\r\n" );
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document.write( "That's too hard to substitute in so, do it on \r\n" );
document.write( "your TI-84:\r\n" );
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document.write( "Type in \r\n" );
document.write( "Press STO \r\n" );
document.write( "Press ALPHA STO ENTER\r\n" );
document.write( "Type in \r\n" );
document.write( "Press ENTER\r\n" );
document.write( "Read 3.\r\n" );
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document.write( "Since 3 is not 5, 3 + sqrt(13) is an EXTRANEOUS answer,\r\n" );
document.write( "so we discard it.\r\n" );
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document.write( "Checking x=3 - sqrt(13) in the original equation:\r\n" );
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document.write( "That's also too hard to substitute in so, do it on \r\n" );
document.write( "your TI-84:\r\n" );
document.write( "\r\n" );
document.write( "Type in \r\n" );
document.write( "Press STO \r\n" );
document.write( "Press ALPHA STO ENTER\r\n" );
document.write( "Type in \r\n" );
document.write( "Press ENTER\r\n" );
document.write( "Read 3.\r\n" );
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document.write( "Since 3 is not 5, 3 - sqrt(13) is also an EXTRANEOUS answer,\r\n" );
document.write( "so we discard it.\r\n" );
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document.write( "The only solutions are 7 and -1.\r\n" );
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document.write( "Edwin
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