document.write( "Question 1111142: If a + b = 11, what are two possible values for c that satisfy the equation below: \r
\n" ); document.write( "\n" ); document.write( "(ax - 4)(bx + 7) = 30x^2 + cx - 28 \n" ); document.write( "

Algebra.Com's Answer #726150 by ikleyn(52810) $\"\"$ $\"About$

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document.write( "After opening the parentheses, you have  ab = 30.\r\n" );
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document.write( "So, actually, you have this system of two equations\r\n" );
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document.write( "a + b = 11,\r\n" );
document.write( "ab    = 30.\r\n" );
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document.write( "There are two pairs of solutions:  (a,b) = (5,6)   and   (a,b) = (6,5).\r\n" );
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document.write( "I found them MENTALLY.\r\n" );
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document.write( "If you want ALGEBRAIC solution, express a = 11-b  from one of the equations and substitute it into the other.\r\n" );
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document.write( "You will get (11-b)*b = 11.\r\n" );
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document.write( "It is a quadratic equation.  Write it in the standard form and solve by any method you want / (you know) / (you like).\r\n" );
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document.write( "After finding \"a\" and \"b\",  \r\n" );
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document.write( "c = 7a - 4b = 7*5-4*6 = 35-24 = 11   or\r\n" );
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document.write( "c = 7a - 4b = 7*6-4*5 = 42-20 = 22.\r\n" );
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document.write( "So, the two possible values for \"c\" are  11  and  22.\r\n" );
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\n" ); document.write( "Ignore writing by @josgarithmetic, since it will lead you to N O W H E R E.\r
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