document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1198815>Question 1198815</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The product of two consecutive integers is 90 less than twice the square of the next larger integer. Find the smaller integer.<BR>\n" );
document.write( "A. 6<BR>\n" );
document.write( "B. 8<BR>\n" );
document.write( "C. 10<BR>\n" );
document.write( "D. 12 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #832459 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3835)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=832459\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "The first sentence translates to this equation<BR>\n" );
document.write( "n(n+1) = 2(n+1)^2-90\r<BR>\n" );
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document.write( "n = first integer<BR>\n" );
document.write( "n+1 = integer right after n\r<BR>\n" );
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document.write( "Let's solve for n.<BR>\n" );
document.write( "n(n+1) = 2(n+1)^2-90<BR>\n" );
document.write( "n^2+n = 2(n^2+2n+1)-90<BR>\n" );
document.write( "n^2+n = 2n^2+4n+2-90<BR>\n" );
document.write( "n^2+n = 2n^2+4n-88<BR>\n" );
document.write( "0 = 2n^2+4n-88-n^2-n<BR>\n" );
document.write( "n^2+3n-88 = 0<BR>\n" );
document.write( "(n+11)(n-8) = 0<BR>\n" );
document.write( "n+11 = 0 or n-8 = 0<BR>\n" );
document.write( "n = -11 or n = 8\r<BR>\n" );
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document.write( "If we focus on the positive values only, then n = -11 is ignored.\r<BR>\n" );
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document.write( "Answer: Choice B<BR>\n" );
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