document.write( "Question 906587: a+2b+3c=12
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Algebra.Com's Answer #550000 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "(1)  a+2b+3c=12\r\n" );
document.write( "(2)  2ab+3ac+6bc=48\r\n" );
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document.write( "Solve (1) for 3c\r\n" );
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document.write( "                          3c = 12-a-2b\r\n" );
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document.write( "            2ab+a(3c)+2b(3c) = 48\r\n" );
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document.write( "Substitute 12-a-2b for 3c\r\n" );
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document.write( "  2ab+a(12-a-2b)+2b(12-a-2b) = 48\r\n" );
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document.write( "2ab+12a-a^2-2ab+24b-2ab-4b^2 = 48\r\n" );
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document.write( "    -a^2-2ab+12a-4b^2+24b-48 = 0\r\n" );
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document.write( "     a^2+2ab-12a+4b^2-24b+48 = 0\r\n" );
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document.write( "     a^2+2ab-12a+4b^2-24b+48 = 0\r\n" );
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document.write( "    a^2+(2b-12)a+4b^2-24b+48 = 0\r\n" );
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document.write( "Calculate the discriminant B^2-4AC with A=1, B=2b-12, C=4b^2-24b+48\r\n" );
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document.write( "B^2-4AC =\r\n" );
document.write( "(2b-12)^2-4(1)(4b^2-24b+48) =\r\n" );
document.write( "(2b-12)^2-4(4b^2-24b+48) =\r\n" );
document.write( "4b^2-48b+144-16b^2+96b-192 =\r\n" );
document.write( "-12b^2+48b-48 =\r\n" );
document.write( "-12(b^2-4b-4) =\r\n" );
document.write( "-12(b-2)^2\r\n" );
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document.write( "In order for this discriminant to be non-negative,\r\n" );
document.write( "it must be 0\r\n" );
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document.write( "-12(b-2)^2 = 0\r\n" );
document.write( "   (b-2)^2 = 0\r\n" );
document.write( "         b = 2\r\n" );
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document.write( "Substitute b=2 in (1)\r\n" );
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document.write( "  a+2b+3c = 12\r\n" );
document.write( "a+2(2)+3c = 12\r\n" );
document.write( "   a+4+3c = 12\r\n" );
document.write( "     a+3c = 8\r\n" );
document.write( "(3)     a = 8-3c\r\n" );
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document.write( "Substitute b=2 in (1)\r\n" );
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document.write( "          2ab+3ac+6bc = 48\r\n" );
document.write( "      2a(2)+3ac+6(2)c = 48\r\n" );
document.write( "(4)        4a+3ac+12c = 48\r\n" );
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document.write( "Substitute 8-3c for a in (4)\r\n" );
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document.write( "  4(8-3c)+3(8-3c)c+12c = 48\r\n" );
document.write( "  4(8-3c)+3c(8-3c)+12c = 48   \r\n" );
document.write( "   32-12c+24c-9c^2+12c = 48\r\n" );
document.write( "          -9c^2+24c+32 = 48\r\n" );
document.write( "          -9c^2+24c-16 = 0\r\n" );
document.write( "           9c^2-24c+16 = 0\r\n" );
document.write( "          (3c-4)(3c-4) = 0\r\n" );
document.write( "                  3c-4 = 0\r\n" );
document.write( "                    3c = 4\r\n" );
document.write( "                     c = 4/3\r\n" );
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document.write( "(3)       a = 8-3c\r\n" );
document.write( "          a = 8-3(4/3)\r\n" );
document.write( "          a = 8-4\r\n" );
document.write( "          a = 4  \r\n" );
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document.write( "So a=4, b=2, c=4/3\r\n" );
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document.write( "Answer a+b+c = 4+2+4/3 = 12/3+6/3+4/3 = 22/3\r\n" );
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document.write( "Edwin
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