document.write( "Question 117946: Hi, this question is a multiple choice question from the pre-ACT test. I don't even know where to start with this one, I tried solving for x, and I tried to put the answer choices in the problem, but to no avail. I believe this is an identity but I can't figure out how to use that knowledge to solve this. This problem has frustrated me for 2 days.\r
\n" ); document.write( "\n" ); document.write( "In the equation, x^2 + 16x + a = (x + b)^2, a and b are constants. If the equation is true for all values of x, what is the value of a?\r
\n" ); document.write( "\n" ); document.write( "the answer choices are: 4, 8, 16, 64, or 256. The correct answer is 64 but I have no idea how to work out the problem to get that answer. Please help me figure this problem out.
\n" ); document.write( "thanks for your help! \n" ); document.write( "
Algebra.Com's Answer #85966 by Edwin McCravy(20054)\"\" \"About 
You can put this solution on YOUR website!
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document.write( " x² + 16x + a = (x + b)²\r\n" );
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document.write( " x² + 16x + a = (x + b)(x + b)\r\n" );
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document.write( " x² + 16x + a = x² + bx + bx + b²\r\n" );
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document.write( " x² + 16x + a = x² + 2bx + b²\r\n" );
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document.write( "Since the left and right sides must be\r\n" );
document.write( "equal for all values of x, the corresponding\r\n" );
document.write( "terms on each side must be equal for all x.\r\n" );
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document.write( "So we have \r\n" );
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document.write( " x² = x²\r\n" );
document.write( "16x = 2bx\r\n" );
document.write( "  a = b²\r\n" );
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document.write( "The second equation tells us 16 = 2b or b = 8\r\n" );
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document.write( "Substituting b = 8 into the third equation\r\n" );
document.write( "gives  \r\n" );
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document.write( "a = b²\r\n" );
document.write( "a = 8²\r\n" );
document.write( "a = 64\r\n" );
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document.write( "Edwin
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