document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=866123>Question 866123</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a rectangle has a length that is 5 less than twice the width.if the rectangle has an area of 63, find the length and width.<BR>\n" );
document.write( "I am having trouble figuring out how to set up this problem I would be very grateful if someone could help me.<BR>\n" );
document.write( "  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #522109 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=522109\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w ALIGN=MIDDLE  ALT=\"w\"   DISABLED_style= \"max-width:90%; height:auto;\" >= width of the rectangle (in whatever units of length they use)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2w ALIGN=MIDDLE  ALT=\"2w\"   DISABLED_style= \"max-width:90%; height:auto;\" >= twice the width<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2w-5 ALIGN=MIDDLE  ALT=\"2w-5\"   DISABLED_style= \"max-width:90%; height:auto;\" >= length of the rectangle (it is 5 less than twice the width)<BR>\n" );
document.write( "The area of the rectangle is length times width, so it is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282w-5%29w=63 ALIGN=MIDDLE  ALT=\"%282w-5%29w=63\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "That is the equation to solve, but we re-arrange it.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282w-5%29w=63 ALIGN=MIDDLE  ALT=\"%282w-5%29w=63\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2w%5E2-5w=63 ALIGN=MIDDLE  ALT=\"2w%5E2-5w=63\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2w%5E2-5w-63=0 ALIGN=MIDDLE  ALT=\"2w%5E2-5w-63=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now it looks like a standard <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc=0 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > quadratic equation and we can solve it using the quadratic formula:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "except that instead of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > we have <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w ALIGN=MIDDLE  ALT=\"w\"   DISABLED_style= \"max-width:90%; height:auto;\" > , and we have<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=2 ALIGN=MIDDLE  ALT=\"a=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > , <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-5 ALIGN=MIDDLE  ALT=\"b=-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > , and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=-63 ALIGN=MIDDLE  ALT=\"c=-63\"   DISABLED_style= \"max-width:90%; height:auto;\" > , so<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w+=+%28-%28-5%29+%2B-+sqrt%28%28-5%29%5E2-4%2A2%2A%28-63%29%29%29%2F%282%2A2%29=%285+%2B-+sqrt%2825%2B504%29%29%2F4=%285+%2B-+sqrt%28529%29%29%2F4=%285+%2B-+23%29%2F4 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The two solutions for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2w%5E2-5w-63=0 ALIGN=MIDDLE  ALT=\"2w%5E2-5w-63=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > are<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w=%285+%2B+23%29%2F4=28%2F4=highlight%287%29 ALIGN=MIDDLE  ALT=\"w=%285+%2B+23%29%2F4=28%2F4=highlight%287%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and<BR>\n" );
document.write( "(5 - 23)/4=-18/4=-9/2}}} ,<BR>\n" );
document.write( "but since the width of the rectangle must be a positive number,<BR>\n" );
document.write( "we must discard <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w=-9%2F2 ALIGN=MIDDLE  ALT=\"w=-9%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > , and the solution is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28w=7%29 ALIGN=MIDDLE  ALT=\"highlight%28w=7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > , along with<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=length=2w-5=2%2A7-5=14-5=highlight%289%29 ALIGN=MIDDLE  ALT=\"length=2w-5=2%2A7-5=14-5=highlight%289%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "The same <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2w%5E2-5w-63=0 ALIGN=MIDDLE  ALT=\"2w%5E2-5w-63=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > quadratic equation can be solved by other means.<BR>\n" );
document.write( "Ypu could \"complete the square\" (not so easy),<BR>\n" );
document.write( "or you could solve it by factoring <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2w%5E2-5w-63 ALIGN=MIDDLE  ALT=\"2w%5E2-5w-63\"   DISABLED_style= \"max-width:90%; height:auto;\" > (if you are good at factoring).<BR>\n" );
document.write( "Factoring:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2w%5E2-5w-63=%282w%5E2-14w%29%2B%289w-63%29=2w%28w-7%29%2B9%28w-7%29=%282w%2B9%29%28w-7%29 ALIGN=MIDDLE  ALT=\"2w%5E2-5w-63=%282w%5E2-14w%29%2B%289w-63%29=2w%28w-7%29%2B9%28w-7%29=%282w%2B9%29%28w-7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2w%5E2-5w-63=0 ALIGN=MIDDLE  ALT=\"2w%5E2-5w-63=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be written as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282w%2B9%29%28w-7%29=0 ALIGN=MIDDLE  ALT=\"%282w%2B9%29%28w-7%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "which is true if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%282w%2B9=0%2C%22or%22%2Cw-7=0%29 ALIGN=MIDDLE  ALT=\"system%282w%2B9=0%2C%22or%22%2Cw-7=0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and those two options lead us to the solutions<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w=-9%2F2%2C+%22or%22%2C+w=7%29 ALIGN=MIDDLE  ALT=\"w=-9%2F2%2C+%22or%22%2C+w=7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > found above.<BR>\n" );
document.write( " <BR>\n" );
document.write( "Completing the square:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2w%5E2-5w-63=0 ALIGN=MIDDLE  ALT=\"2w%5E2-5w-63=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><--><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2w%5E2-5w=63 ALIGN=MIDDLE  ALT=\"2w%5E2-5w=63\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "dividing both sides of the equal sign by 2,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w%5E2-%285%2F2%29w=63%2F2 ALIGN=MIDDLE  ALT=\"w%5E2-%285%2F2%29w=63%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w%5E2-%285%2F2%29w%2B%285%2F4%29%5E2=63%2F2%2B%285%2F4%29%5E2 ALIGN=MIDDLE  ALT=\"w%5E2-%285%2F2%29w%2B%285%2F4%29%5E2=63%2F2%2B%285%2F4%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28w-5%2F4%29%5E2=63%2F2%2B25%2F16 ALIGN=MIDDLE  ALT=\"%28w-5%2F4%29%5E2=63%2F2%2B25%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28w-5%2F4%29%5E2=504%2F16%2B25%2F16 ALIGN=MIDDLE  ALT=\"%28w-5%2F4%29%5E2=504%2F16%2B25%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28w-5%2F4%29%5E2=529%2F16 ALIGN=MIDDLE  ALT=\"%28w-5%2F4%29%5E2=529%2F16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28w-5%2F4=sqrt%28529%2F16%29=sqrt%28529%29%2Fsqrt%2816%29=23%2F4%2C%22or%22%2Cw-5%2F4=-sqrt%28529%2F16%29=-sqrt%28529%29%2Fsqrt%2816%29=-23%2F4%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which means that<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28w=23%2F4%2B5%2F4=28%2F4=7%2C%22or%22%2Cw=-23%2F4%2B5%2F4=-18%2F4=-9%2F2%29 ALIGN=MIDDLE  ALT=\"system%28w=23%2F4%2B5%2F4=28%2F4=7%2C%22or%22%2Cw=-23%2F4%2B5%2F4=-18%2F4=-9%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );