document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=68069>Question 68069</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I have asked this question within the past two days without a response. I am having a tough time figuring out how to set this problem up. Once I know how to set it up and why, I can probably solve the equation. I hope someone out there can help me with this one, please.\r<BR>\n" );
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document.write( "Find two consecutive positive integers such that the sum of their squares is 85. [You must use algebra to solve this, setting up an equation with a variable, and using algebra to solve for the variable.] </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #48368 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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=48368\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x be the first positive integer.  The next consecutive positive integer would then be x+1.<BR>\n" );
document.write( "The sum of the squares of these is 85.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+%28x%2B1%29%5E2+=+85 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+%28x%2B1%29%5E2+=+85\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify and solve for x.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+%28x%5E2+%2B+2x+%2B+1%29+=+85 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+%28x%5E2+%2B+2x+%2B+1%29+=+85\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2+%2B+2x+%2B+1+=+85 ALIGN=MIDDLE  ALT=\"2x%5E2+%2B+2x+%2B+1+=+85\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 85 from both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2+%2B+2x+-+84+=+0 ALIGN=MIDDLE  ALT=\"2x%5E2+%2B+2x+-+84+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide through by 2.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E1+%2B+x+-+42+=+0 ALIGN=MIDDLE  ALT=\"x%5E1+%2B+x+-+42+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B7%29%28x-6%29+=+0 ALIGN=MIDDLE  ALT=\"%28x%2B7%29%28x-6%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Apply the zero product principle.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B7+=+0 ALIGN=MIDDLE  ALT=\"x%2B7+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and/or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-6+=+0 ALIGN=MIDDLE  ALT=\"x-6+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So, x = -7 and x = 6  Discard the negative value as the problem requires positive integers.<BR>\n" );
document.write( "The two integers are: 6 and 7\r<BR>\n" );
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document.write( "Check:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%5E2+%2B+7%5E2+=+36+%2B+49 ALIGN=MIDDLE  ALT=\"6%5E2+%2B+7%5E2+=+36+%2B+49\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=85 ALIGN=MIDDLE  ALT=\"85\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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