document.write( "Question 33038: Can you please solve this for me? I have to solve this using factoring:\r
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Algebra.Com's Answer #853875 by ikleyn(53742) $\"\"$ $\"About$

You can put this solution on YOUR website!
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\n" ); document.write( "Can you please solve this for me? I have to solve this using factoring:
\n" ); document.write( "The sum of the squares of two consecutive negative even integers is 340. Find the integers.
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\n" ); document.write( "\n" ); document.write( " I will solve it in as simple way as I can.\r
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document.write( "We are looking for two consecutive even integer numbers n and (n+2).\r\n" );
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document.write( "I will start from the central integer number 'm' between n and (n+2), so that\r\n" );
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document.write( "    n = m-1,  n+2 = m+1.\r\n" );
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document.write( "Then my equation is\r\n" );
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document.write( "    (m-1)^2 + (m+1)^2 = 340,\r\n" );
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document.write( "    (m^2 - 2m + 1) + (m^2 + 2m + 1) = 340,\r\n" );
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document.write( "     2m^2 + 2 = 340,\r\n" );
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document.write( "     2m^2 = 340 - 2 = 338,\r\n" );
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document.write( "      m^2 = 338/2 = 169,\r\n" );
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document.write( "      m = +/-  = +/- 13.\r\n" );
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document.write( "We are looking for two consecutive negative numbers, so these numbers are -14 and - 12.    ANSWER\r\n" );
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document.write( "CHECK.  (-14)^2 + (-12)^2 = 196 + 144 = 340.    ! Precisely correct !\r\n" );
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\n" ); document.write( "\n" ); document.write( "Notice that the other tutor reduced the problem to solution of a quadratic equation, but left the solution to you.\r
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\n" ); document.write( "\n" ); document.write( "I solved the problem completely in a simplest way, practically mentally
\n" ); document.write( "to the end, without solving a quadratic equation.\r
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