document.write( "Question 944238: Pls assist in solving:\"+16x%5E%28-3%29+=+2x%5E%28-6%29+\" \n" ); document.write( "
Algebra.Com's Answer #575704 by Edwin McCravy(20060)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "The other tutor's answer above is incorrect.  The other tutor gave the\r\n" );
document.write( "solution for \"+%2816x%29%5E%28-3%29+=+%282x%29%5E%28-6%29+\".  The 2 and the 16 are not in\r\n" );
document.write( "parentheses so they are not raised to those negative powers.  Only x is\r\n" );
document.write( "raised to those negative powers in your equation.\r\n" );
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document.write( "\"+16x%5E%28-3%29+=+2x%5E%28-6%29+\"\r\n" );
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document.write( "Divide both sides by 2\r\n" );
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document.write( "\"+8x%5E%28-3%29+=+x%5E%28-6%29+\"\r\n" );
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document.write( "Write the factors with negative exponents as denominator\r\n" );
document.write( "factors with positive exponents:\r\n" );
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document.write( "\"+8%2Fx%5E3+=+1%2Fx%5E6+\"\r\n" );
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document.write( "Cross-multiply:\r\n" );
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document.write( "\"8x%5E6=x%5E3\"\r\n" );
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document.write( "Get 0 on the right sides:\r\n" );
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document.write( "\"8x%5E6-x%5E3=0\"\r\n" );
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document.write( "Factor out x³\r\n" );
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document.write( "\"x%5E3%288x%5E3-1%29=0\"\r\n" );
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document.write( "\"x%5E3=0\",  \"8x%5E3-1=0\"\r\n" );
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document.write( "\"x=0\",    \"%282x%29%5E3-1%5E3=0\"\r\n" );
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document.write( "0 is not a solution because 0 may only be raised to \r\n" );
document.write( "positive powers, and the original has negative powers.\r\n" );
document.write( "The second equation requires the factorization of the\r\n" );
document.write( "difference of two cubes:\r\n" );
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document.write( "              \"%282x-1%29%28%282x%29%5E2%2B2x%2A1%2B1%5E2%29\"\r\n" );
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document.write( "              \"%282x-1%29%284x%5E2%2B2x%2B1%29\"\r\n" );
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document.write( "              \"2x-1=0\"   \"4x%5E2%2B2x%2B1=0\"\r\n" );
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document.write( "              \"2x=1\"     \"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"\r\n" );
document.write( "             \r\n" );
document.write( "              \"x=1%2F2\"    \"x+=+%28-2+%2B-+sqrt%28+2%5E2-4%2A4%2A1+%29%29%2F%282%2A4%29+\"\r\n" );
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document.write( "                             \"x+=+%28-2+%2B-+sqrt%284-16+%29%29%2F8+\"\r\n" );
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document.write( "                             \"x+=+%28-2+%2B-+sqrt%28-12+%29%29%2F8+\"\r\n" );
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document.write( "                             \"x+=+%28-2+%2B-+i%2Asqrt%2812+%29%29%2F8+\"\r\n" );
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document.write( "                             \"x+=+%28-2+%2B-+i%2Asqrt%284%2A3+%29%29%2F8+\"\r\n" );
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document.write( "                             \"x+=+%28-2+%2B-+2i%2Asqrt%283+%29%29%2F8+\"\r\n" );
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document.write( "                             \"x+=+%282%28-1+%2B-+i%2Asqrt%283+%29%29%29%2F8+\"\r\n" );
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document.write( "                             \"x+=+%28-1+%2B-+i%2Asqrt%283%29%29%2F4\"\r\n" );
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document.write( "So there are three solutions \"1%2F2\", \"%28-1+%2B+i%2Asqrt%283%29%29%2F4\", \"%28-1+-+i%2Asqrt%283%29%29%2F4\"  \r\n" );
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document.write( "Edwin
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