document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=148699>Question 148699</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/9780073052816/algebrahomeworkh>Beginning and Intermediate Algebra</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> I am supposed to use applications of quadratic equations to solve this problem, I have worked on it about five hours now, and cannot figure it out. So I figure I am not translating the English correctly, could you please show me how to translate this. <BR>\n" );
document.write( "   The sum of the squares of two consecutive integers is nine less than ten times the sum of the integars. Find all such integers. <BR>\n" );
document.write( "      What I did says    x^2(x+1)^2=10x+9   or I also used 10(x+9)<BR>\n" );
document.write( "Please help me, this is making me nuts! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #109033 by </B><A HREF=/tutors/aboutme.mpl?userid=ptaylor><B>ptaylor(2198)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ptaylor><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/cgi-bin/show-face.mpl?user=ptaylor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=109033\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x=one integer; x^2 is the square of the integer<BR>\n" );
document.write( "Then x+1=the other integer; (x+1)^2 is the square of the other integer\r<BR>\n" );
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document.write( "x+(x+1)=2x+1 is the sum of the integers 10(2x+1)=10 times the sum of the integers;10(2x+1)-9=9 less than 10 times the sum of the integer. So our equation to solve is:\r<BR>\n" );
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document.write( "x^2+(x+1)^2=10(2x+1)-9 simplify<BR>\n" );
document.write( "x^2+x^2+2x+1=20x+10-9<BR>\n" );
document.write( "2x^2+2x+1=20x+1 subtract 20x and also 1 from each side\r<BR>\n" );
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document.write( "2x^2+2x+1-1-20x=20x-20x+1-1 collect like terms\r<BR>\n" );
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document.write( "2x^2-18x=0  divide each term by 2<BR>\n" );
document.write( "x^2-9x=0<BR>\n" );
document.write( "x(x-9)=0<BR>\n" );
document.write( "x=0; x+1=1<BR>\n" );
document.write( "and<BR>\n" );
document.write( "x=9; x+1=10\r<BR>\n" );
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document.write( "CK<BR>\n" );
document.write( "0^2+1^2=10(0+1)-9<BR>\n" );
document.write( "1=1<BR>\n" );
document.write( "and<BR>\n" );
document.write( "9^2+10^2=10(19)-9<BR>\n" );
document.write( "81+100=190-9<BR>\n" );
document.write( "181=181\r<BR>\n" );
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document.write( "Hope this helps---ptaylor<BR>\n" );
document.write( " </SPAN>\n" );
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