document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1158426>Question 1158426</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A boat travels 2 km upstream and 2 km back. The time for the round trip is 4 hrs. The speed of the stream is 5 ​km/hr. What is the speed of the boat in still​ water? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #781376 by </B><A HREF=/tutors/aboutme.mpl?userid=Shin123><B>Shin123(626)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Shin123><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=Shin123><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=781376\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's say that the boat can travel x km/hr on still water. It can travel (x-5) km/hr upstream and (x+5) km/hr downstream. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F%28x-5%29%2B2%2F%28x%2B5%29=4 ALIGN=MIDDLE  ALT=\"2%2F%28x-5%29%2B2%2F%28x%2B5%29=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28x%2B5%29%2F%28x-5%29%28x%2B5%29%2B2%28x-5%29%2F%28x-5%29%28x%2B5%29=4%28x%2B5%29%28x-5%29%2F%28x%2B5%29%28x-5%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28x%2B5%29%2B2%28x-5%29=4%28x-5%29%28x%2B5%29 ALIGN=MIDDLE  ALT=\"2%28x%2B5%29%2B2%28x-5%29=4%28x-5%29%28x%2B5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%2B10%2B2x-10=4x%5E2-100 ALIGN=MIDDLE  ALT=\"2x%2B10%2B2x-10=4x%5E2-100\"   DISABLED_style= \"max-width:90%; height:auto;\" >. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2-4x-100=0 ALIGN=MIDDLE  ALT=\"4x%5E2-4x-100=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-x-25=0 ALIGN=MIDDLE  ALT=\"x%5E2-x-25=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > <TABLE  BORDER=1>\n" );
document.write( "\n" );
document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=complete_square.solver>COMPLETING THE SQUARE solver for quadratics</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Read <A  rel=nofollow HREF=Fool-Proof-Completing-the-Square-Part-I.lesson>this lesson on completing the square by prince_abubu</A>, if you do not know how to complete the square.<BR>Let's convert <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1x%5E2%2B-1x%2B-25=0 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-1x%2B-25=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > to standard form by dividing both sides by 1: <BR>\n" );
document.write( "We have: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1x%5E2%2B-1x%2B-25=0 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-1x%2B-25=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \n" );
document.write( "What we want to do now is to change this equation to a complete square <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2Bsomenumber%29%5E2+%2B+othernumber ALIGN=MIDDLE  ALT=\"%28x%2Bsomenumber%29%5E2+%2B+othernumber\"   DISABLED_style= \"max-width:90%; height:auto;\" >. How can we find out values of <B>somenumber</B> and <B>othernumber</B> that would make it work?<BR>\n" );
document.write( "Look at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2Bsomenumber%29%5E2 ALIGN=MIDDLE  ALT=\"%28x%2Bsomenumber%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2Bsomenumber%29%5E2+=+x%5E2%2B2%2Asomenumber%2Ax+%2B+somenumber%5E2 ALIGN=MIDDLE  ALT=\"%28x%2Bsomenumber%29%5E2+=+x%5E2%2B2%2Asomenumber%2Ax+%2B+somenumber%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Since the coefficient in our equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1x%5E2%2Bhighlight_red%28+-1%29+%2A+x%2B-25=0 ALIGN=MIDDLE  ALT=\"1x%5E2%2Bhighlight_red%28+-1%29+%2A+x%2B-25=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > that goes in front of x is -1, we know that -1=2*somenumber, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=somenumber+=+-1%2F2 ALIGN=MIDDLE  ALT=\"somenumber+=+-1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So, we know that our equation can be rewritten as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B-1%2F2%29%5E2+%2B+othernumber ALIGN=MIDDLE  ALT=\"%28x%2B-1%2F2%29%5E2+%2B+othernumber\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and we do not yet know the other number.<BR>\n" );
document.write( "We are almost there. Finding the other number is simply a matter of not making too many mistakes. We need to find 'other number' such that  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B-1%2F2%29%5E2+%2B+othernumber ALIGN=MIDDLE  ALT=\"%28x%2B-1%2F2%29%5E2+%2B+othernumber\"   DISABLED_style= \"max-width:90%; height:auto;\" > is equivalent to our original equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1x%5E2%2B-1x%2Bhighlight_green%28+-25+%29=0 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-1x%2Bhighlight_green%28+-25+%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B-1%2F2%29%5E2+%2B+othernumber+=+x%5E2%2B-1x%2Bhighlight_red%28+-1%5E2%2F4%2Bothernumber+%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  The highlighted <FONT COLOR=red>red part</FONT> must be equal to -25 (highlighted <FONT COLOR=green>green part</FONT>).<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%5E2%2F4+%2B+othernumber+=+-25 ALIGN=MIDDLE  ALT=\"-1%5E2%2F4+%2B+othernumber+=+-25\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=othernumber+=+-25--1%5E2%2F4+=+-25.25 ALIGN=MIDDLE  ALT=\"othernumber+=+-25--1%5E2%2F4+=+-25.25\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "So, the equation converts to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B-1%2F2%29%5E2+%2B+-25.25+=+0 ALIGN=MIDDLE  ALT=\"%28x%2B-1%2F2%29%5E2+%2B+-25.25+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B-1%2F2%29%5E2+=+25.25 ALIGN=MIDDLE  ALT=\"%28x%2B-1%2F2%29%5E2+=+25.25\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "    Our equation converted to a square <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B-1%2F2%29%5E2 ALIGN=MIDDLE  ALT=\"%28x%2B-1%2F2%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, equated to a number (25.25).<BR>\n" );
document.write( "  <BR>\n" );
document.write( "    Since the right part 25.25 is greater than zero, there are two solutions:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "     <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28+%28x%2B-1%2F2%29+=+%2Bsqrt%28+25.25+%29%2C+%28x%2B-1%2F2%29+=+-sqrt%28+25.25+%29+%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    , or<BR>\n" );
document.write( "  <BR>\n" );
document.write( "     <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28+%28x%2B-1%2F2%29+=+5.02493781056044%2C+%28x%2B-1%2F2%29+=+-5.02493781056044+%29 ALIGN=MIDDLE  ALT=\"system%28+%28x%2B-1%2F2%29+=+5.02493781056044%2C+%28x%2B-1%2F2%29+=+-5.02493781056044+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "     <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28+x%2B-1%2F2+=+5.02493781056044%2C+x%2B-1%2F2+=+-5.02493781056044+%29 ALIGN=MIDDLE  ALT=\"system%28+x%2B-1%2F2+=+5.02493781056044%2C+x%2B-1%2F2+=+-5.02493781056044+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "     <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28+x+=+5.02493781056044--1%2F2%2C+x+=+-5.02493781056044--1%2F2+%29 ALIGN=MIDDLE  ALT=\"system%28+x+=+5.02493781056044--1%2F2%2C+x+=+-5.02493781056044--1%2F2+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <BR>\n" );
document.write( "     <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28+x+=+5.52493781056044%2C+x+=+-4.52493781056044+%29 ALIGN=MIDDLE  ALT=\"system%28+x+=+5.52493781056044%2C+x+=+-4.52493781056044+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Answer: x=5.52493781056044, -4.52493781056044.\n" );
document.write( "</TD></TR>\n" );
document.write( "</TABLE>\n" );
document.write( " <br/> The boat can travel about 5.525 km/hr. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );