document.write( "Question 1209247: Find the constant p such that x^2 - 5x - 14x + x^2 + p is the square of a binomial. \n" ); document.write( "

Algebra.Com's Answer #847914 by ikleyn(52784) $\"\"$ $\"About$

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\n" ); document.write( "Find the constant p such that x^2 - 5x - 14x + x^2 + p is the square of a binomial.
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document.write( "Reduce to the standard form quadratic polynomial by combining like terms\r\n" );
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document.write( "    2x^2 - 19x + p.\r\n" );
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document.write( "Present it as a square of a binomial\r\n" );
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document.write( "    2x^2 - 19x + p = (ax+b)^2.\r\n" );
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document.write( "It is the same as\r\n" );
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document.write( "    2x^2 - 19x + p = a^2*x^2 + 2abx + b^2.\r\n" );
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document.write( "Hence,\r\n" );
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document.write( "    2   = a^2,  or  a = ;\r\n" );
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document.write( "    -19 = 2ab,  or  -19 = ,  which gives  b =  = ;\r\n" );
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document.write( "    p = b^2 =  = .\r\n" );
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