document.write( "Question 1105803: Find the Values of A,B,C,D and E so that each equation is an identity (Show your solution)
\n" ); document.write( "4x^2 - 9y^2 - 24x + 18y + 27 = A(x-B)^2 + C(y+D)^2 + E \n" ); document.write( "

Algebra.Com's Answer #720713 by ikleyn(52800) $\"\"$ $\"About$

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document.write( "   4x^2 - 9y^2 - 24x + 18y + 27 = \r\n" );
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document.write( "= (4x^2 - 24x) - (9y^2 - 18y) + 27 = \r\n" );
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document.write( "= 4(x^2 - 6x) - 9*(y^2 - 2y) + 27 = \r\n" );
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document.write( "= 4*(x^2 - 6x + 9) - 9*(y^2 - 2y + 1) + 27 - 4*9 + 9*1 = \r\n" );
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document.write( "= 4*(x-3)^2 - 9*(y-1)^2 + 0.\r\n" );
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document.write( "Comparing it with the expression  A(x-B)^2 + C(y+D)^2 + E,  you can conclude that\r\n" );
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document.write( "Answer.  A = 4,  B = 3,  C = 9,  D = 1, E = 0.\r\n" );
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