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document.write( "I am having trouble figuring out how to solve this problem.\r
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document.write( "Find all real solutions to the equation 40-106e^x+101e^2x-41e^3x+6e^4x=0.
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document.write( "Let us introduce new variable z = 
, Then the equation will take a form\r\n" );
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document.write( "p(z) = 6z^4 - 41z^3 +101z^2 - 106z + 40 = 0.\r\n" );
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document.write( "One root is z=1. You can check it making direct calculation.\r\n" );
document.write( "So, the polynomial has the divisor (z-1).\r\n" );
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document.write( "The quotient 
is q(z) = 
(long division).\r\n" );
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document.write( "The root of the cubic polynomial is z=2. You can check it making direct calculation.\r\n" );
document.write( "So, the polynomial has the divisor (z-2).\r\n" );
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document.write( "The quotient 
is r(z) = 
(long division).\r\n" );
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document.write( "r(z) has the roots 2.5 and 
(quadratic formula).\r\n" );
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document.write( "So, the polynomial p(z) has the roots 1, 2, 2.5 and .\r\n" );
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document.write( "Since z = 
, the original polynomial has the roots \r\n" );
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document.write( "x = ln(1) = 0, x = ln(2), x = ln(2.5) and x = ln((3/4)).\r\n" );
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document.write( "Solved.\r
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