document.write( "Question 599451: The product of two consecutive even integers is 224. Find the integers \n" ); document.write( "

Algebra.Com's Answer #378953 by Edwin McCravy(20055) $\"\"$ $\"About$

You can put this solution on YOUR website!
The product of two consecutive even integers is 224. Find the integers
\n" ); document.write( "

\r\n" );
document.write( "I'll show you two ways to do it.  One way your teacher won't accept and one that\r\n" );
document.write( "he or she will accept\"\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Here's the easy way that your teacher won't accept.  They have to both be\r\n" );
document.write( "close to the square root of 224.  So we find the square root of 224 with a\r\n" );
document.write( "calculator and get 14.966629555.  So we take the two consecutive even integers\r\n" );
document.write( "that 14.966629555 is between and we get that 14.966629555 is between the two\r\n" );
document.write( "consecutive integers 14 and 16. So they are one of the answers.  But another \r\n" );
document.write( "solution is found by taking the negatives of those, -16 and -14, since their\r\n" );
document.write( "product is also +224.  Your teacher won't accept this way but it's a good\r\n" );
document.write( "way to know when you've got the right answer.\r\n" );
document.write( "\r\n" );
document.write( "Here's the way your teacher will accept:\r\n" );
document.write( "\r\n" );
document.write( "Let x represent the smaller consecutive even integer\r\n" );
document.write( "Then x + 2 represents the larger consecutive even integer\r\n" );
document.write( "\r\n" );
document.write( "               x(x + 2) = 224\r\n" );
document.write( "\r\n" );
document.write( "                x² + 2x = 224\r\n" );
document.write( "\r\n" );
document.write( "          x² + 2x - 224 = 0\r\n" );
document.write( "\r\n" );
document.write( "       (x - 14)(x + 16) = 0\r\n" );
document.write( "\r\n" );
document.write( "    x - 14 = 0;                   x + 16 = 0\r\n" );
document.write( "\r\n" );
document.write( "         x = 14;                      x = -16\r\n" );
document.write( "       \r\n" );
document.write( " x+2 = 14 + 2 = 16;            x+2 = -16 + 2 = -14; \r\n" );
document.write( " \r\n" );
document.write( "So there are two solutions (14 and 16) and (-16 and -14)\r\n" );
document.write( "\r\n" );
document.write( "Edwin

\n" ); document.write( " \n" ); document.write( "

\n" );