document.write( "Question 80619: If twelve is added to six times a number, the result is twenty-eight less than the square of the number. Find all such numbers. \n" ); document.write( "

Algebra.Com's Answer #57850 by ptaylor(2198) $\"\"$ $\"About$

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\n" ); document.write( "Let x=the number
\n" ); document.write( "x^2= the square of the number; 28 less is x^2-28
\n" ); document.write( "Six times the number is 6x and when we add 12 we get 6x+12\r
\n" ); document.write( "\n" ); document.write( "We are told that:\r
\n" ); document.write( "\n" ); document.write( "6x+12=x^2-28 subtract 6x and also 12 from both sides\r
\n" ); document.write( "\n" ); document.write( "6x-6x+12-12=x^2-6x-12-28 collect like terms\r
\n" ); document.write( "\n" ); document.write( "0=x^2-6x-40 or x^2-6x-40=0 quadratic in standard form and it can be factored:\r
\n" ); document.write( "\n" ); document.write( "(Note: When the A coefficient of a quadratic is 1, then the B coefficient will be the sum of the factors of the C coefficient, if it is factorable. In this case the factors of -40 that add up to -6 are -10 and +4)\r
\n" ); document.write( "\n" ); document.write( "(x-10)(x+4)=0\r
\n" ); document.write( "\n" ); document.write( "x=10
\n" ); document.write( "and
\n" ); document.write( "x=-4\r
\n" ); document.write( "\n" ); document.write( "CK
\n" ); document.write( "for x=10
\n" ); document.write( "6(10)+12=10^2-28
\n" ); document.write( "72=72
\n" ); document.write( "for x=-4
\n" ); document.write( "6(-4)+12=(-4)^2-28
\n" ); document.write( "-24+12=16-28
\n" ); document.write( "-12=-12\r
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\n" ); document.write( "\n" ); document.write( "Hope this helps----ptaylor\r
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