document.write( "Question 892250: Im having problems with this equation:\r
\n" ); document.write( "\n" ); document.write( "Two sets of quadratic expressions are shown below in various forms:\r
\n" ); document.write( "\n" ); document.write( "Line 1: x2 + 3x + 2 (x + 1)(x + 2) (x + 1.5)2 − 0.25
\n" ); document.write( "Line 2: x2 + 5x + 6 (x + 2)(x + 3) (x + 2.5)2 + 6.25\r
\n" ); document.write( "\n" ); document.write( "Which line contains three equivalent expressions? \r
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\n" ); document.write( "\n" ); document.write( "Line 1 only \r
\n" ); document.write( "\n" ); document.write( "Line 2 only \r
\n" ); document.write( "\n" ); document.write( "Both Line 1 and Line 2 \r
\n" ); document.write( "\n" ); document.write( "Neither Line 1 nor Line 2 \r
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Algebra.Com's Answer #540392 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Line 1: x² + 3x + 2,  (x + 1)(x + 2),  (x + 1.5)² − 0.25\r\n" );
document.write( "Line 2: x² + 5x + 6,  (x + 2)(x + 3),  (x + 2.5)² + 6.25\r\n" );
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document.write( "If two expressions are equivalent, then no matter what number\r\n" );
document.write( "we substitute into them, they will always simplify to the\r\n" );
document.write( "same numbers.\r\n" );
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document.write( "So let's check by substituting a value, say, x=0 in each:\r\n" );
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document.write( "Line 1: 0² + 3(0) + 2,  (0 + 1)(0 + 2),  (0 + 1.5)² − 0.25\r\n" );
document.write( "Line 1:             2,               2,        2.25 − 0.25\r\n" );
document.write( "Line 1:             2,               2,                  2 \r\n" );
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document.write( "Line 2: 0² + 5(0) + 6,  (0 + 2)(0 + 3),  (0 + 2.5)² + 6.25\r\n" );
document.write( "Line 2:             6,               6,        6.25 + 6.25\r\n" );
document.write( "Line 2:             6,               6,              12.50\r\n" );
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document.write( "Looks like the answer is Line 1 only.  We have eliminated Line 2.\r\n" );
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document.write( "But we can't be sure about Line 1.  That's because it might \r\n" );
document.write( "have just been an accident that we got the same.  So let's \r\n" );
document.write( "substitute x=1 in each:\r\n" );
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document.write( "Line 1: 1² + 3(1) + 2,  (1 + 1)(1 + 2),  (1 + 1.5)² − 0.25\r\n" );
document.write( "Line 1:         1+3+2,             2·3,      (2.5)² − 0.25\r\n" );
document.write( "Line 1:             6,               6,        6.25 - 0.25 \r\n" );
document.write( "Line 1:             6,               6,                  6\r\n" );
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document.write( "Yes it's probably Line 1 only. For it's not \r\n" );
document.write( "likely that we'd have run into two \r\n" );
document.write( "accidents.\r\n" );
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document.write( "Try x = 2\r\n" );
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document.write( "Line 1: 2² + 3(2) + 2,  (2 + 1)(2 + 2),  (2 + 1.5)² − 0.25\r\n" );
document.write( "Line 1:         4+6+2,             3·4,      (3.5)² − 0.25\r\n" );
document.write( "Line 1:            12,              12,       12,25 - 0.25 \r\n" );
document.write( "Line 1:            12,              12,                 12\r\n" );
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document.write( "No doubt about it.  It's Line 1 only.\r\n" );
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document.write( "Edwin
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