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Consecutive integers are 1 apart from each other. So if
\n" ); document.write( "x = the first integer
\n" ); document.write( "then
\n" ); document.write( "x+1 = the next integer
\n" ); document.write( "The product of two consecutive integers:
\n" ); document.write( "x*(x+1)
\n" ); document.write( "The product of two consecutive integers is decreased by 20 times the greater integer:
\n" ); document.write( "x*(x+1) - 20*(x+1)
\n" ); document.write( "The product of two consecutive integers is decreased by 20 times the greater integer [is} 442:
\n" ); document.write( "x*(x+1) - 20*(x+1) = 442
\n" ); document.write( "Now that we have translated the problem into an equation we can solve it. First we simplify each side:
\n" ); document.write( "
\n" ); document.write( "
\n" ); document.write( "This is a quadratic equation so we want one side to be zero. So we'll subtract 442 from each side:
\n" ); document.write( "
\n" ); document.write( "Now we factor (or use the Quadratic Formula):
\n" ); document.write( "(x-33)(x+14) = 0
\n" ); document.write( "From the Zero Product Property we know that this (or any) product can be zero only if one (or more) factors is zero. So:
\n" ); document.write( "x-33 = 0 or x+14 = 0
\n" ); document.write( "Solving these we get:
\n" ); document.write( "x = 33 or x = -14
\n" ); document.write( "These are not consecutive integers. But they are not supposed to be! \"x\" is the first of the two integers. x+1 is the other integer. So we have two sets of answers, one for when x = 33 and the other for when x = -14:
\n" ); document.write( "33 and 34
\n" ); document.write( "or
\n" ); document.write( "-14 and -13
\n" ); document.write( " \n" ); document.write( "