document.write( "Question 49224: How do you solve this expression:\r
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Algebra.Com's Answer #32644 by AnlytcPhil(1807)\"\" \"About 
You can put this solution on YOUR website!
How do you solve this expression: \r\n" );
document.write( "3x^2-5x+2 can be factor as 3(x+p)^2=q\r\n" );
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document.write( "I think you mistyped.  I think you meant\r\n" );
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document.write( "How do you solve this expression: \r\n" );
document.write( "3x²-5x+2 can be factored as 3(x + p)² + q\r\n" );
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document.write( "Then let's multiply 3(x + p)² + q out and\r\n" );
document.write( "see what p and q would have to be\r\n" );
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document.write( "3(x + p)² + q =\r\n" );
document.write( "3(x + p)(x + p) + q =\r\n" );
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document.write( "3(x² + 2px + p²) + q =\r\n" );
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document.write( "3x² + 6px + 3p² + q =\r\n" );
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document.write( "Now compare that to \r\n" );
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document.write( "3x² - 5x + 2.\r\n" );
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document.write( "Now I'll do some coloring to make it clear:\r\n" );
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document.write( "3x² + 6px + 3p² + q =\r\n" );
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document.write( "Now compare that to \r\n" );
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document.write( "3x² - 5x + 2.\r\n" );
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document.write( "For those to be equal, those two red parts\r\n" );
document.write( "must be equal and also those two blue parts\r\n" );
document.write( "must be equal. IOW\r\n" );
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document.write( "          6p = -5\r\n" );
document.write( "     3p² + q =  2\r\n" );
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document.write( "To solve that system, solve the first for p\r\n" );
document.write( "          6p = -5 \r\n" );
document.write( "           p = -5/6\r\n" );
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document.write( "Now substitute -5/6 for p in\r\n" );
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document.write( "     3p² + q =  2\r\n" );
document.write( "3(-5/6)² + q = 2\r\n" );
document.write( "3(25/36) + q = 2\r\n" );
document.write( "   25/12 + q = 2\r\n" );
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document.write( "Clear of fractions by multiplying thru by 12\r\n" );
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document.write( "    25 + 12q = 24\r\n" );
document.write( "         12q = -1\r\n" );
document.write( "           q = -1/12\r\n" );
document.write( "               \r\n" );
document.write( "Therefore, p = -5/6 and q = -1/12. Therefore,\r\n" );
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document.write( "3x²-5x+2 can be factored as 3(x - 5/6)² - 1/12\r\n" );
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document.write( "Edwin
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