document.write( "Question 1209149: For what real values of c is x^2 - 8x - 16x + c + 24x^2 the square of a binomial? \n" ); document.write( "
Algebra.Com's Answer #847734 by Edwin McCravy(20055)\"\" \"About 
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For what real values of c is x^2 - 8x - 16x + c + 24x^2 the square of a binomial?
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document.write( "First let's combine like terms:\r\n" );
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document.write( "\"25x%5E2-24x%2Bc\"\r\n" );
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document.write( "So if it is to factor as the square of a binomial, there is \r\n" );
document.write( "some number a such that this is an identity:\r\n" );
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document.write( "\"%285x+%2B+a%29%285x+%2B+a%29\"\"%22%22=%22%22\"\"25x%5E2-24x%2Bc\"\r\n" );
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document.write( "\"25x%5E2%2B10ax%2Ba%5E2\"\"%22%22=%22%22\"\"25x%5E2-24x%2Bc\"\r\n" );
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document.write( "So for them to be identical, we must have:\r\n" );
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document.write( "\"10a=-24\"} and \"a%5E2=c\"\r\n" );
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document.write( "\"a=-24%2F10=-12%2F5\" and \"c=a%5E2=%28-12%2F5%29%5E2=144%2F25\"\r\n" );
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document.write( "Answer: c = 144/25\r\n" );
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document.write( "Edwin
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