document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=669649>Question 669649</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find three consecutive odd integers such that the square of the largest integer is 25 more than three times the sum of the smaller numbers. Give your answers as comma-separated numbers in ascending order.\r<BR>\n" );
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document.write( "I have tried everything I learned to answer this question, but I just seem to keep getting stuck around here(if I did it right):X^2-6x-15=0\r<BR>\n" );
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document.write( "Please help if possible it it my last question and it is due at midnight! Thank you!!<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #416518 by </B><A HREF=/tutors/aboutme.mpl?userid=DrBeeee><B>DrBeeee(684)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=DrBeeee><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=416518\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You must have had an error. The correct quadratic is<BR>\n" );
document.write( "(1) x^2 + 2*x - 15 = 0, which has roots at<BR>\n" );
document.write( "(2) x = {-5,3}, where we can get two solution <BR>\n" );
document.write( "sequences<BR>\n" );
document.write( "(3) (-5,-3,-1) and (3,5,7)<BR>\n" );
document.write( "To check use<BR>\n" );
document.write( "(4) (x+4)^2 = 25 + 3*(x + x + 2)<BR>\n" );
document.write( "Is ((-1)^2 = 25+3*(-5-3))?<BR>\n" );
document.write( "Is (1 = 25 + 3*(-8))?<BR>\n" );
document.write( "Is (1 = 25 - 24)?<BR>\n" );
document.write( "Is (1 = 1)? Yes<BR>\n" );
document.write( "Is (7^2 = 25+3*(3+5))?<BR>\n" );
document.write( "Is (49 = 25+3*8)?<BR>\n" );
document.write( "Is (49 = 49)? Yes<BR>\n" );
document.write( "Answer: There are two sequences of consecutive odd intergers that satisfy the problem statement - (-5,-3,-1) and (3,5,7).<BR>\n" );
document.write( "Let me derive (1) so you may find your error.<BR>\n" );
document.write( "Let x = the first odd integer<BR>\n" );
document.write( "Then the next odd integer is x + 2 and the third is x + 4.<BR>\n" );
document.write( "The problem statement has<BR>\n" );
document.write( "(5) (x+4)^2 = 25 + 3*(x + x+2) or<BR>\n" );
document.write( "(6) x^2 + 8*x + 16 = 25 + 3*(x + x+2) or<BR>\n" );
document.write( "(7) x^2 + 8*x + 16 = 25 + 6*x + 6 or<BR>\n" );
document.write( "(8) x^2 + 2*x - 15 = 0 which agrees with (1)<BR>\n" );
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