document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=286294>Question 286294</A>: <I><SPAN STYLE=\"word-break: break-all;\"> When one integer is added to the square of the next consecutive integer, the sum is 41. Find the integers.\r<BR>\n" );
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document.write( "Please show how to solve this? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #207608 by </B><A HREF=/tutors/aboutme.mpl?userid=oberobic><B>oberobic(2304)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=oberobic><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=207608\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The answer that springs to mind is 5 + 6*6 = 41.<BR>\n" );
document.write( "But that tells the story without showing the work.<BR>\n" );
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document.write( "x = one integer<BR>\n" );
document.write( "x+1 = the next consecutive integer<BR>\n" );
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document.write( "x + (x+1)^2 = 41<BR>\n" );
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document.write( "Collect terms and simplify<BR>\n" );
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document.write( "x + x^2 + 2x + 1 = 41<BR>\n" );
document.write( "x^2 + 3x -40 = 0<BR>\n" );
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document.write( "factor<BR>\n" );
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document.write( "(x+8)(x-5) = 0<BR>\n" );
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document.write( "So we have TWO possible answers:  x= -8, x=5.<BR>\n" );
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document.write( "5 and 6 is one answer, as mentioned above and confirmed.<BR>\n" );
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document.write( "But by doing the work, we have another candidate.<BR>\n" );
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document.write( "With quadratic terms you sometimes get what are called spurious answers:  answers that cannot be correct.  The answer x= -8  might not work, but let's check it.<BR>\n" );
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document.write( "-8 + -7^2 = -8 + 49 = 41<BR>\n" );
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document.write( "Correct!  That show how important it is to do and to show the work.<BR>\n" );
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document.write( "Answer:<BR>\n" );
document.write( "The two consecutive integers are 5 and 6 or -8 and -7.<BR>\n" );
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document.write( "Done. </SPAN>\n" );
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