document.write( "Question 714477: Show me x squared + x cubed = 810
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Algebra.Com's Answer #438809 by Edwin McCravy(20054)\"\" \"About 
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document.write( "x² + x³ = 810\r\n" );
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document.write( "Rearrange in descending order:\r\n" );
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document.write( "x³ + x² - 810 = 0\r\n" );
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document.write( "If it has any rational solutions, they will be ± factors\r\n" );
document.write( "of 810, which are:\r\n" );
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document.write( "±1, ±2, ±3, ±5, ±6, ±9, ±10, ±15, ±18, ±27, ±30, ±45,\r\n" );
document.write( "±54, ±81, ±90, ±135, ±162, ±270, ±405, ±810\r\n" );
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document.write( "It has one sign change so it has 1 positive solution.\r\n" );
document.write( "So we'll try the positive values with synthetic division.\r\n" );
document.write( "Notice that we have to put in a place holder for there\r\n" );
document.write( "is no x term, so we consider the equation as \r\n" );
document.write( "x³ + x² + 0x - 810 = 0\r\n" );
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document.write( "We try 1:\r\n" );
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document.write( "1|1  1  0  -810\r\n" );
document.write( " |   1  2     2  \r\n" );
document.write( "  1  2  2  -808  No\r\n" );
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document.write( "We try 2:\r\n" );
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document.write( "2|1  1  0  -810\r\n" );
document.write( " |   2  6    12  \r\n" );
document.write( "  1  3  6  -798  No\r\n" );
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document.write( "We try 3:\r\n" );
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document.write( "3|1  1   0  -810\r\n" );
document.write( " |   3  12    36  \r\n" );
document.write( "  1  4  12  -774  No\r\n" );
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document.write( "We try 5:\r\n" );
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document.write( "5|1  1   0  -810\r\n" );
document.write( " |   5  30   150  \r\n" );
document.write( "  1  6  30  -660  No \r\n" );
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document.write( "We try 6:\r\n" );
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document.write( "6|1  1   0  -810\r\n" );
document.write( " |   6  42   252  \r\n" );
document.write( "  1  7  42  -558  No\r\n" );
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document.write( "We try 9:\r\n" );
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document.write( "9|1  1   0  -810\r\n" );
document.write( " |   9  90   810  \r\n" );
document.write( "  1 10  90     0  YES!\r\n" );
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document.write( "So x³ + x² - 810 = 0 factors as\r\n" );
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document.write( "(x - 9)(x² + 10x + 90) = 0\r\n" );
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document.write( "We use the zero-factor principle:\r\n" );
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document.write( "x - 9 = 0;  x² + 10x + 90\r\n" );
document.write( "    x = 9;  x = \"%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"\r\n" );
document.write( "            x = \"%28-10+%2B-+sqrt%28+10%5E2-4%2A1%2A90+%29%29%2F%282%2A1%29+\"\r\n" );
document.write( "            x = \"%28-10+%2B-+sqrt%28100+-360+%29%29%2F2+\"\r\n" );
document.write( "            x = \"%28-10+%2B-+sqrt%28-260+%29%29%2F2+\"\r\n" );
document.write( "            x = \"%28-10+%2B-+i%2Asqrt%28260+%29%29%2F2+\"\r\n" );
document.write( "            x = \"%28-10+%2B-+i%2Asqrt%284%2A65+%29%29%2F2+\"\r\n" );
document.write( "            x = \"%28-10+%2B-+2i%2Asqrt%2865+%29%29%2F2+\"\r\n" );
document.write( "            x = \"%282%28-5+%2B-+i%2Asqrt%2865+%29%29%29%2F2+\"\r\n" );
document.write( "            x = \"%28cross%282%29%28-5+%2B-+i%2Asqrt%2865+%29%29%29%2Fcross%282%29+\"\r\n" );
document.write( "            x = \"-5+%2B-+i%2Asqrt%2865+%29\"\r\n" );
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document.write( "Three solutions, one real and two imaginary:\r\n" );
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document.write( "9, \"-5+%2B+i%2Asqrt%2865+%29\", and \"-5+-+i%2Asqrt%2865+%29\"\r\n" );
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document.write( "Edwin
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