document.write( "Question 1098842: The sequence x-12,2x-15,3x+30... Is a geometric progression. Find the sum of all possible values of x. \n" ); document.write( "

Algebra.Com's Answer #713284 by ikleyn(52781) $\"\"$ $\"About$

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document.write( "Since the given sequence is a geometric progression, the ratio   is the same as the ratio \r\n" );
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document.write( "and both are equal to the common ratio.  It gives you an equation\r\n" );
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document.write( " = .\r\n" );
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document.write( "To solve it, cross multiply\r\n" );
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document.write( "(2x-15)*(2x-15) = (x-12)*(3x+30),  ====>\r\n" );
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document.write( "4x^2 - 30x + 225 = 3x^2 -36x + 30x - 360  ====>\r\n" );
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document.write( "x^2 - 24x + 585 = 0.\r\n" );
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document.write( "Do not hurry to solve this quadratic equation.\r\n" );
document.write( "You do not need do it.\r\n" );
document.write( "They ask you about the sum of all possible solutions.\r\n" );
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document.write( "Apply the Vieta's theorem, which says that the sum of all roots of this equation is equal to the coefficient at \"x\" taken with the opposite sign.\r\n" );
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document.write( "Therefore, you answer is  24.\r\n" );
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