document.write( "Question 69111: If twice the square of a positive integer is 12 more than 10 times that integer, what is the integer? \n" ); document.write( "

Algebra.Com's Answer #49183 by rmromero(383) $\"\"$ $\"About$

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document.write( "What is asked in the problem?\r\n" );
document.write( "What is the integer?\r\n" );
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document.write( "Given:\r\n" );
document.write( "Twice the square of a positive integer is 12 more than 10 times that integer.\r\n" );
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document.write( "Representation:\r\n" );
document.write( "Let x = the integer\r\n" );
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document.write( "Write an Equation.Translate the sentence into mathematical equation\r\n" );
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document.write( "Twice the square of a positive integer is 12 more than 10 times that integer.\r\n" );
document.write( "     2x^2 = 10x + 12\r\n" );
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document.write( "Solve the equation.\r\n" );
document.write( "2x^2 - 10x - 12 = 0           Factor the equation to solve for x.\r\n" );
document.write( "(2x + 2)(x - 6) = 0           Zero product Property.\r\n" );
document.write( "2x + 2 = 2    or   x - 6 = 0\r\n" );
document.write( "    2x = 0    or       x = 6\r\n" );
document.write( "     x = 0    or       x = 6\r\n" );
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document.write( "Checking:\r\n" );
document.write( "  2x^2 = 10x + 12, x= 0\r\n" );
document.write( "2(0)^2 = 10(0) + 12\r\n" );
document.write( "     0 = 0   ----------->> True\r\n" );
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document.write( "  2x^2 = 10x + 12, x=6\r\n" );
document.write( "2(6)^2 = 10(6) + 12\r\n" );
document.write( "     72 = 60 + 12\r\n" );
document.write( "     72 = 72 --------->> True\r\n" );
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document.write( "Therefore the integer is 0 or 6.

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