document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=195949>Question 195949</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The sum of the squares of three consecutive, positive integers is equal to the sum of the squares of the next two integers.  Find the five integers.\r<BR>\n" );
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document.write( "x +  x +2 + x + 3 = x squared + x squared.. is the best I can come up with????  help!  Thanks. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #146919 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=146919\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Consecutive integers follow the form: x, x+1, x+2, x+3, etc...\r<BR>\n" );
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document.write( "So...\r<BR>\n" );
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document.write( "\"The sum of the squares of three consecutive, positive integers is equal to the sum of the squares of the next two integers.\" translates to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B%28x%2B1%29%5E2%2B%28x%2B2%29%5E2=%28x%2B3%29%5E2%2B%28x%2B4%29%5E2 ALIGN=MIDDLE  ALT=\"x%5E2%2B%28x%2B1%29%5E2%2B%28x%2B2%29%5E2=%28x%2B3%29%5E2%2B%28x%2B4%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B%28x%2B1%29%5E2%2B%28x%2B2%29%5E2=%28x%2B3%29%5E2%2B%28x%2B4%29%5E2 ALIGN=MIDDLE  ALT=\"x%5E2%2B%28x%2B1%29%5E2%2B%28x%2B2%29%5E2=%28x%2B3%29%5E2%2B%28x%2B4%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2Bx%5E2%2B2x%2B1%2Bx%5E2%2B4x%2B4=x%5E2%2B6x%2B9%2Bx%5E2%2B8x%2B16 ALIGN=MIDDLE  ALT=\"x%5E2%2Bx%5E2%2B2x%2B1%2Bx%5E2%2B4x%2B4=x%5E2%2B6x%2B9%2Bx%5E2%2B8x%2B16\"   DISABLED_style= \"max-width:90%; height:auto;\" > FOIL\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2%2B6x%2B5=2x%5E2%2B14x%2B25 ALIGN=MIDDLE  ALT=\"3x%5E2%2B6x%2B5=2x%5E2%2B14x%2B25\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2%2B6x%2B5-2x%5E2-14x-25=0 ALIGN=MIDDLE  ALT=\"3x%5E2%2B6x%2B5-2x%5E2-14x-25=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Get all terms to the left side.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-8x-20=0 ALIGN=MIDDLE  ALT=\"x%5E2-8x-20=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
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document.write( "Notice we have a quadratic equation in the form of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=1 ALIGN=MIDDLE  ALT=\"a=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-8 ALIGN=MIDDLE  ALT=\"b=-8\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=-20 ALIGN=MIDDLE  ALT=\"c=-20\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Let's use the quadratic formula to solve for x\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the quadratic formula\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-%28-8%29+%2B-+sqrt%28+%28-8%29%5E2-4%281%29%28-20%29+%29%29%2F%282%281%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28-%28-8%29+%2B-+sqrt%28+%28-8%29%5E2-4%281%29%28-20%29+%29%29%2F%282%281%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=1 ALIGN=MIDDLE  ALT=\"a=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-8 ALIGN=MIDDLE  ALT=\"b=-8\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=-20 ALIGN=MIDDLE  ALT=\"c=-20\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%288+%2B-+sqrt%28+%28-8%29%5E2-4%281%29%28-20%29+%29%29%2F%282%281%29%29 ALIGN=MIDDLE  ALT=\"x+=+%288+%2B-+sqrt%28+%28-8%29%5E2-4%281%29%28-20%29+%29%29%2F%282%281%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Negate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-8 ALIGN=MIDDLE  ALT=\"-8\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8 ALIGN=MIDDLE  ALT=\"8\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%288+%2B-+sqrt%28+64-4%281%29%28-20%29+%29%29%2F%282%281%29%29 ALIGN=MIDDLE  ALT=\"x+=+%288+%2B-+sqrt%28+64-4%281%29%28-20%29+%29%29%2F%282%281%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-8 ALIGN=MIDDLE  ALT=\"-8\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=64 ALIGN=MIDDLE  ALT=\"64\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%288+%2B-+sqrt%28+64--80+%29%29%2F%282%281%29%29 ALIGN=MIDDLE  ALT=\"x+=+%288+%2B-+sqrt%28+64--80+%29%29%2F%282%281%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%281%29%28-20%29 ALIGN=MIDDLE  ALT=\"4%281%29%28-20%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-80 ALIGN=MIDDLE  ALT=\"-80\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%288+%2B-+sqrt%28+64%2B80+%29%29%2F%282%281%29%29 ALIGN=MIDDLE  ALT=\"x+=+%288+%2B-+sqrt%28+64%2B80+%29%29%2F%282%281%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rewrite <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2864--80%29 ALIGN=MIDDLE  ALT=\"sqrt%2864--80%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2864%2B80%29 ALIGN=MIDDLE  ALT=\"sqrt%2864%2B80%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%288+%2B-+sqrt%28+144+%29%29%2F%282%281%29%29 ALIGN=MIDDLE  ALT=\"x+=+%288+%2B-+sqrt%28+144+%29%29%2F%282%281%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=64 ALIGN=MIDDLE  ALT=\"64\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=80 ALIGN=MIDDLE  ALT=\"80\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=144 ALIGN=MIDDLE  ALT=\"144\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%288+%2B-+sqrt%28+144+%29%29%2F%282%29 ALIGN=MIDDLE  ALT=\"x+=+%288+%2B-+sqrt%28+144+%29%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%288+%2B-+12%29%2F%282%29 ALIGN=MIDDLE  ALT=\"x+=+%288+%2B-+12%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=144 ALIGN=MIDDLE  ALT=\"144\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=12 ALIGN=MIDDLE  ALT=\"12\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%288+%2B+12%29%2F%282%29 ALIGN=MIDDLE  ALT=\"x+=+%288+%2B+12%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%288+-+12%29%2F%282%29 ALIGN=MIDDLE  ALT=\"x+=+%288+-+12%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Break up the expression. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2820%29%2F%282%29 ALIGN=MIDDLE  ALT=\"x+=+%2820%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=++%28-4%29%2F%282%29 ALIGN=MIDDLE  ALT=\"x+=++%28-4%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms. \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+10 ALIGN=MIDDLE  ALT=\"x+=+10\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-2 ALIGN=MIDDLE  ALT=\"x+=+-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify. \r<BR>\n" );
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document.write( "So the answers are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+10 ALIGN=MIDDLE  ALT=\"x+=+10\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-2 ALIGN=MIDDLE  ALT=\"x+=+-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "  \r<BR>\n" );
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document.write( "Once again, the problem mentions that the numbers are positive. So this means that the only solution is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+10 ALIGN=MIDDLE  ALT=\"x+=+10\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "This means that the numbers are: 10, 11, 12, 13, and 14 </SPAN>\n" );
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