document.write( "Question 283197: The product of 2 consecutive intergers is 41 more than their sum. find the intergers \n" ); document.write( "
Algebra.Com's Answer #205589 by oberobic(2304)\"\" \"About 
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Two consecutive numbers can be defined as x and y, but a better choice is x and x+1.
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\n" ); document.write( "The product of the two numbers is: x(x+1). We are told this 41 more than the sum.
\n" ); document.write( "The sum of the two numbers is: x + (x+1).
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\n" ); document.write( "So the equation we need to solve is:
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\n" ); document.write( "\n" ); document.write( "x(x+1) = x+(x+1)+41
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\n" ); document.write( "x^2 +x = 2x + 42
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\n" ); document.write( "subtract 2x from both sides
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\n" ); document.write( "x^2 +x -2x = 2x-2x + 42
\n" ); document.write( "x^2 -x = 42
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\n" ); document.write( "subtract 42 from both sides
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\n" ); document.write( "x^2 -x -42 = 42-42 = 0
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\n" ); document.write( "factor
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\n" ); document.write( "(x-7)(x+6) = 0
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\n" ); document.write( "x = 7 or -6
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\n" ); document.write( "We have to check both solutions by substituting these values into the equation.
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\n" ); document.write( "7(7+1) = 7+(7+1)+41 ??
\n" ); document.write( "7*8 =56
\n" ); document.write( "7+8 + 41=56
\n" ); document.write( "Correct
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\n" ); document.write( "-6(-6+1)=-6+(-6+1)+41 ??
\n" ); document.write( "36 -6 = -6 -6 + 42 ??
\n" ); document.write( "30 = 30
\n" ); document.write( "Correct.
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\n" ); document.write( "Answer the consecutive integers are either 7 and 8 OR -6 and -5.
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\n" ); document.write( "Done \n" ); document.write( "
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