document.write( "Question 30560: Solve the equation by making an appropriate substitition.\r
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Algebra.Com's Answer #17218 by AnlytcPhil(1806)\"\" \"About 
You can put this solution on YOUR website!
Solve the equation by making an appropriate substitition. \r\n" );
document.write( "             x4 - 14x2 - 32 = 0 \r\n" );
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document.write( "The \"literal part\" of a term is the term without its numerical coefficient.\r\n" );
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document.write( "If the literal part of the first term happens to be the square of the literal\r\n" );
document.write( "part of the second term, then we substitute w for the literal part of the\r\n" );
document.write( "second term and w2 for the literal part of the first term.\r\n" );
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document.write( "The first term is 1x4, and so its literal part is just the x4 part without the\r\n" );
document.write( "coefficient 1.\r\n" );
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document.write( "The second term is -14x2, and so its literal part is just the x2 part without\r\n" );
document.write( "the coefficient -14.\r\n" );
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document.write( "Notice that x4 just happens to be the square of x2. so we substitute w2 for x4\r\n" );
document.write( "and w for x2, so the original equation\r\n" );
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document.write( "        x4 - 14x2 - 32 = 0\r\n" );
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document.write( "becomes\r\n" );
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document.write( "         w2 - 14w - 32 = 0\r\n" );
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document.write( "To factor the left side we think of two numbers which have product -32 and\r\n" );
document.write( "sum -14.  These are -16 and +2.  So the above factors as\r\n" );
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document.write( "       (w - 16)(w + 2) = 0\r\n" );
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document.write( "Then we use the zero factor property and set each factor = 0\r\n" );
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document.write( "Setting w - 16 = 0 gives w = 16\r\n" );
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document.write( "Setting w + 2 = 0 gives w = -2\r\n" );
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document.write( "However we don't want w, we want x.  So we now replace w by x2 in each\r\n" );
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document.write( "             w = 16                    w = -2                   \r\n" );
document.write( "            x2 = 16                   x2 = -2__\r\n" );
document.write( "             x = ±4                    x = ±Ö-2\r\n" );
document.write( "                                       x = ±iÖ2\r\n" );
document.write( "                                      _         _\r\n" );
document.write( "So there are four solutions: 4, -4, iÖ2, and -iÖ2\r\n" );
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document.write( "Edwin\r\n" );
document.write( "AnlytcPhil@aol.com
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