document.write( "Question 38351: State the quadratic formula and hence solve x(x+3) = 6x + 2\r
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Algebra.Com's Answer #23835 by AnlytcPhil(1806)\"\" \"About 
You can put this solution on YOUR website!
State the quadratic formula and hence solve \r\n" );
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document.write( "x(x + 3) = 6x + 2\r\n" );
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document.write( "Please show your working out, and thank you in \r\n" );
document.write( "advance for your help\r\n" );
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document.write( "Quadratic formula:\r\n" );
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document.write( "Given Ax² + Bx + C = 0, the solutions are\r\n" );
document.write( "           ________ \r\n" );
document.write( "     -B ± ÖB² - 4AC\r\n" );
document.write( "x = —————————————————\r\n" );
document.write( "           2A\r\n" );
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document.write( "     x(x + 3) = 6x + 2\r\n" );
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document.write( "      x² + 3x = 6x + 2\r\n" );
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document.write( "Get 0 on right by subtracting 6x and 2 from both sides\r\n" );
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document.write( "  x² - 3x - 2 = 0 \r\n" );
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document.write( "Put 1 in front of x²\r\n" );
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document.write( " 1x² - 3x - 2 = 0\r\n" );
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document.write( "Compare that equation to\r\n" );
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document.write( " Ax² + Bx + C = 0\r\n" );
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document.write( "We see that A = 1, B = -3, and C = -2\r\n" );
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document.write( "Substituting in \r\n" );
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document.write( "           ________ \r\n" );
document.write( "     -B ± ÖB² - 4AC\r\n" );
document.write( "x = —————————————————\r\n" );
document.write( "           2A\r\n" );
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document.write( "              ________________ \r\n" );
document.write( "     -(-1) ± Ö(-1)² - 4(1)(-2)\r\n" );
document.write( "x = ———————————————————————————\r\n" );
document.write( "              2(1)\r\n" );
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document.write( "          _____ \r\n" );
document.write( "     1 ± Ö1 + 8\r\n" );
document.write( "x = ————————————\r\n" );
document.write( "          2\r\n" );
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document.write( "          _ \r\n" );
document.write( "     1 ± Ö9\r\n" );
document.write( "x = ————————\r\n" );
document.write( "       2\r\n" );
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document.write( "           \r\n" );
document.write( "     1 ± 3\r\n" );
document.write( "x = ————————\r\n" );
document.write( "       2\r\n" );
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document.write( "± means + or -\r\n" );
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document.write( "First solution uses +:\r\n" );
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document.write( "     1 + 3     4\r\n" );
document.write( "x = ——————— = ——— = 2\r\n" );
document.write( "       2       2\r\n" );
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document.write( "Second solution uses -:\r\n" );
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document.write( "     1 - 3     -2\r\n" );
document.write( "x = ——————— = ————— = -1\r\n" );
document.write( "       2        2\r\n" );
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document.write( "Notice that your problem COULD have been solved\r\n" );
document.write( "simply by factoring:\r\n" );
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document.write( "      x(x + 3) = 6x + 2\r\n" );
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document.write( "       x² + 3x = 6x + 2\r\n" );
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document.write( "   x² - 3x - 2 = 0\r\n" );
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document.write( "(x + 1)(x - 2) = 0\r\n" );
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document.write( "Using 0 factor principle:\r\n" );
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document.write( "x + 1 = 0, so x = -1\r\n" );
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document.write( "x - 2 = 0, so x = 2\r\n" );
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document.write( "However you were told to solve it by the\r\n" );
document.write( "quadratic formula to get practice because\r\n" );
document.write( "most quadratic equations can't be solved\r\n" );
document.write( "by factoring.\r\n" );
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document.write( "Edwin\r\n" );
document.write( "AnlytcPhil@aol.com
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