document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=325632>Question 325632</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The product of two positive consecutive  integers is 41 more than their sum. Find the integers. \r<BR>\n" );
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document.write( "(I have gotten this far, but do not know how to show the next step.)\r<BR>\n" );
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document.write( "first integer = x<BR>\n" );
document.write( "second integer = x+1<BR>\n" );
document.write( "+ 41 more their sum =<BR>\n" );
document.write( "=<BR>\n" );
document.write( "x(x+1) = 41 + x + x + 1<BR>\n" );
document.write( "=<BR>\n" );
document.write( "x^2 + x = 42 + 2x<BR>\n" );
document.write( "=<BR>\n" );
document.write( "x^2 + x - (2x) = 42 + 2x - (2x)<BR>\n" );
document.write( "=<BR>\n" );
document.write( "x^2 - x = 42<BR>\n" );
document.write( "=<BR>\n" );
document.write( "x^2 - x - (42) = 42 - (42)<BR>\n" );
document.write( "=<BR>\n" );
document.write( "x^2 - x - 42 = 0<BR>\n" );
document.write( "= ??????\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #233148 by </B><A HREF=/tutors/aboutme.mpl?userid=jessica43><B>jessica43(140)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jessica43><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=233148\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You have set up the problem correctly, now all you have to do factor the trinomial x^2 - x - 42.<BR>\n" );
document.write( "Factoring a trinomial is the opposite of the FOIL method. The factors will have this form:<BR>\n" );
document.write( "(x A)(x B)<BR>\n" );
document.write( "where A and B will be the factors of the third term (42). The factors of 42 are: 1, 2, 3, 6, 7, 14, 21, and 42. So these are our possibilities of A and B: 1&42, 2&21, 3&14, 6&7.<BR>\n" );
document.write( "Now, we need to see what combination, when added, will equal -1 (since the second term of our trinomial is -x).<BR>\n" );
document.write( "We know that one number must be negative because when multiplied they equal a negative number. So the only combination that could equal -1 when added is -7 and 6.<BR>\n" );
document.write( "So:<BR>\n" );
document.write( "x^2 - x - 42 = 0<BR>\n" );
document.write( "(x-7)(x+6)= 0<BR>\n" );
document.write( "So for this to equal zero, x = 7 or x = -6.<BR>\n" );
document.write( "Since the problem states that the answer is a positive integer, x cannot equal -6.<BR>\n" );
document.write( "So x=7 and the two consecutive integers are 7 and 8. </SPAN>\n" );
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