document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=59202>Question 59202</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find two consecutive positive integers such that the sum of their square is 85.<BR>\n" );
document.write( "Your help will be very appreciated!<BR>\n" );
document.write( "Thanks so much!<BR>\n" );
document.write( "ac </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #40603 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=40603\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let the consecutive integers equal x and x+1<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;\" ><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;\" ><BR>\n" );
document.write( "This can be solved either by the quadratic formula<BR>\n" );
document.write( "of by completing the square. I'll complete the square<BR>\n" );
document.write( "subtract 1 from both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2+%2B+2x+=+84 ALIGN=MIDDLE  ALT=\"2x%5E2+%2B+2x+=+84\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "divide both sides by 2<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+x+=+42 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+x+=+42\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "to complete the square, take one-half of the coeffecient<BR>\n" );
document.write( "of x, square it, and add it to both sides<BR>\n" );
document.write( "Half of 1 is 1/2 and (1/2)^2 = 1/4<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+x+%2B+1%2F4+=+42+%2B+1%2F4 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+x+%2B+1%2F4+=+42+%2B+1%2F4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+%2B+1%2F2%29%5E2+=+%28168+%2B+1%29%2F+4 ALIGN=MIDDLE  ALT=\"%28x+%2B+1%2F2%29%5E2+=+%28168+%2B+1%29%2F+4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B+1%2F2+=+%280+%2B-+sqrt%28169%29%29+%2F+2 ALIGN=MIDDLE  ALT=\"x+%2B+1%2F2+=+%280+%2B-+sqrt%28169%29%29+%2F+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2B13%2F2+-+1%2F2 ALIGN=MIDDLE  ALT=\"x+=+%2B13%2F2+-+1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2B12%2F2 ALIGN=MIDDLE  ALT=\"x+=+%2B12%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2B6 ALIGN=MIDDLE  ALT=\"x+=+%2B6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-13%2F2+-+1%2F2 ALIGN=MIDDLE  ALT=\"x+=+-13%2F2+-+1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-14%2F2 ALIGN=MIDDLE  ALT=\"x+=+-14%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-7 ALIGN=MIDDLE  ALT=\"x+=+-7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The problem wants 2 consecutive POSITIVE integers, so I'll<BR>\n" );
document.write( "pick x = +6<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B+1+=+%2B7 ALIGN=MIDDLE  ALT=\"x+%2B+1+=+%2B7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The answers are +6 and +7<BR>\n" );
document.write( "check:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%5E2+%2B+7%5E2+=+85 ALIGN=MIDDLE  ALT=\"6%5E2+%2B+7%5E2+=+85\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36+%2B+49+=+85 ALIGN=MIDDLE  ALT=\"36+%2B+49+=+85\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=85+=+85 ALIGN=MIDDLE  ALT=\"85+=+85\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "OK </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );