document.write( "Question 1148732: My math teacher didn't teach us how in the world to do this I am completely stuck.\r
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\n" ); document.write( "\n" ); document.write( "The sum of 6 times a positive number and 1 is the same as the square of 1 less than the number.\r
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Algebra.Com's Answer #770075 by ikleyn(52786) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( "Let the unknown number be \"x\".\r\n" );
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document.write( "Then  6 times this number is 6x;  6 times this number and 1 is  (6x +1).\r\n" );
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document.write( "From the other side, \"the square of 1 less than the number\" is  (x-1)^2.\r\n" );
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document.write( "These expressions, (6x+1) and (s-1)^2, \"are the same\", which means that they are equal at this x\r\n" );
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document.write( "    6x+1 = (x-1)^2.     (1)\r\n" );
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document.write( "The equation is done; now your task is to solve it.\r\n" );
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document.write( "    6x+1 = x^2 - 2x + 1\r\n" );
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document.write( "    x^2 - 8x = 0\r\n" );
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document.write( "    x*(x-8) = 0.\r\n" );
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document.write( "It has two roots:  x= 0  and x= 8.\r\n" );
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document.write( "Only x= 8 is POSITIVE.  (x= 0 IS NOT positive (!) )\r\n" );
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document.write( "So your answer is  x= 8.\r\n" );
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document.write( "CHECK.  Left side of equation (1)  is 6x+1 = 6*8+1 = 49.\r\n" );
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document.write( "        Right side of equation (1) is  (x-1)^2 = (8-1)^2 = 7^2 = 49.\r\n" );
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document.write( "        Both sides are equal --- hence, the equation solved correctly.\r\n" );
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document.write( "        The wording formulation is satisfied --- hence, the problem is solved CORRECTLY.   (!)\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved, explained, answered and completed.\r
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\n" ); document.write( "\n" ); document.write( "Come again to this forum soon to learn something new (!)\r
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\n" ); document.write( "\n" ); document.write( " Or to learn something better (!)\r
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