document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=978430>Question 978430</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the length and width of a rectangle are (3x+1) and (2x-1)cm respectively.If the area of the rectangle is 144cm,find x<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 #599933 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=599933\">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=%283x%2B1%29+%282x-1%29=144 ALIGN=MIDDLE  ALT=\"%283x%2B1%29+%282x-1%29=144\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%5E2-3x%2B2x-1=144 ALIGN=MIDDLE  ALT=\"6x%5E2-3x%2B2x-1=144\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%5E2-x-1=144 ALIGN=MIDDLE  ALT=\"6x%5E2-x-1=144\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%5E2-x-1-144=0 ALIGN=MIDDLE  ALT=\"6x%5E2-x-1-144=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%5E2-x-145=0 ALIGN=MIDDLE  ALT=\"6x%5E2-x-145=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "We need to solve the quadratic equation above.<BR>\n" );
document.write( "Quadratic equations can always be solved<BR>\n" );
document.write( "by \"completing the square\"<BR>\n" );
document.write( "and by applying the quadratic formula.<BR>\n" );
document.write( "Some quadratic equations can also be solved by factoring,<BR>\n" );
document.write( "and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%5E2-x-145=0 ALIGN=MIDDLE  ALT=\"6x%5E2-x-145=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > is one of those.<BR>\n" );
document.write( "To factor, we look for factors of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2A145 ALIGN=MIDDLE  ALT=\"6%2A145\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "No need to multiply, when we can find and recombine the prime factors:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2A145=%282%2A3%29%2A%285%2A29%29=%282%2A3%2A5%29%2A29=30%2A29 ALIGN=MIDDLE  ALT=\"6%2A145=%282%2A3%29%2A%285%2A29%29=%282%2A3%2A5%29%2A29=30%2A29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%5E2-x-145=6x%5E2-30x%2B29x-145=%286x%5E2-30x%29%2B%2829x-145%29=6x%28x-5%29%2B29%28x-5%29=%286x%2B29%29%28x-5%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So we can re-write <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6x%5E2-x-145=0 ALIGN=MIDDLE  ALT=\"6x%5E2-x-145=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286x%2B29%29%28x-5%29=0 ALIGN=MIDDLE  ALT=\"%286x%2B29%29%28x-5%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%286x%2B29=0%2C%22or%22%2Cx-5=0%29 ALIGN=MIDDLE  ALT=\"system%286x%2B29=0%2C%22or%22%2Cx-5=0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28x=-29%2F6%2C%22or%22%2Cx=5%29 ALIGN=MIDDLE  ALT=\"system%28x=-29%2F6%2C%22or%22%2Cx=5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=5 ALIGN=MIDDLE  ALT=\"x=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%282x-1=2%2A5-1=10-1=9%2C3x%2B1=3%2A5%2B1=15%2B1=16%29 ALIGN=MIDDLE  ALT=\"system%282x-1=2%2A5-1=10-1=9%2C3x%2B1=3%2A5%2B1=15%2B1=16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "for the length and width of the rectangle to be 16 and 9cm respectively,<BR>\n" );
document.write( "which makes perfect sense, so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=5%29 ALIGN=MIDDLE  ALT=\"highlight%28x=5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a good answer.<BR>\n" );
document.write( "On the other hand,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-29%2F6 ALIGN=MIDDLE  ALT=\"x=-29%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" >---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%282x-1=2%2A%28-29%2F6%29-1=-29%2F3-1=-32%2F3%2C3x%2B1=3%2A%28-29%2F6%29%2B1=-29%2F2%2B1=-27%2F2%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "yielding negative numbers for the length and width of the rectangle, does not make sense.<BR>\n" );
document.write( "So, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-29%2F6 ALIGN=MIDDLE  ALT=\"x=-29%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a solution for the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283x%2B1%29+%282x-1%29=144 ALIGN=MIDDLE  ALT=\"%283x%2B1%29+%282x-1%29=144\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "but is not a solution to the word problem. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );