document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=886874>Question 886874</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the solution for this?<BR>\n" );
document.write( "Please use the 4 methods in quadratic equation to see the answer:<BR>\n" );
document.write( "*extracting the square root<BR>\n" );
document.write( "*Factoring<BR>\n" );
document.write( "*Completing the square<BR>\n" );
document.write( "and *Quadratic Formula\r<BR>\n" );
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document.write( "The length of a rectangular garden is one more than thrice it's width. Its area is 80 m^2. Find the length and the width.\r<BR>\n" );
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document.write( "Much thanks! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #536217 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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=536217\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Assigning variables,<BR>\n" );
document.write( "Length is L, width is w.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=1%2B3w ALIGN=MIDDLE  ALT=\"L=1%2B3w\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=wL=80 ALIGN=MIDDLE  ALT=\"wL=80\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  Substitution for L gives <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w%283w%2B1%29=80 ALIGN=MIDDLE  ALT=\"w%283w%2B1%29=80\"   DISABLED_style= \"max-width:90%; height:auto;\" >,  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3w%5E2%2Bw=80 ALIGN=MIDDLE  ALT=\"3w%5E2%2Bw=80\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%283w%5E2%2Bw-80=0%29 ALIGN=MIDDLE  ALT=\"highlight_green%283w%5E2%2Bw-80=0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You can try to factor that.  Product -80 will have various combinations but you need to also have<BR>\n" );
document.write( "the coefficient of 3 on the leading term.<BR>\n" );
document.write( "For 80:   20 & 4, 2 & 40, 8 & 10, ... others.<BR>\n" );
document.write( "Easiest to avoid trying to factorize.<BR>\n" );
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document.write( "COMPLETE THE SQUARE-----<BR>\n" );
document.write( "First factor the 3.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%28w%5E2%2B%281%2F3%29w-80%2F3%29=0 ALIGN=MIDDLE  ALT=\"3%28w%5E2%2B%281%2F3%29w-80%2F3%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The term to use is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F6%29%5E2 ALIGN=MIDDLE  ALT=\"%281%2F6%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >   (Reading-up on this will help);<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%28w%5E2%2B%281%2F3%29w%2B1%2F36-1%2F36-80%2F3%29=0 ALIGN=MIDDLE  ALT=\"3%28w%5E2%2B%281%2F3%29w%2B1%2F36-1%2F36-80%2F3%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%28%28w%2B1%2F6%29%5E2-%281%2F36%2B80%2F3%29%29=0 ALIGN=MIDDLE  ALT=\"3%28%28w%2B1%2F6%29%5E2-%281%2F36%2B80%2F3%29%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%28%28w%2B1%2F6%29%5E2-%28961%2F36%29%29=0 ALIGN=MIDDLE  ALT=\"3%28%28w%2B1%2F6%29%5E2-%28961%2F36%29%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%28w%2B1%2F6%29%5E2-961%2F12=0 ALIGN=MIDDLE  ALT=\"3%28w%2B1%2F6%29%5E2-961%2F12=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%28w%2B1%2F6%29%5E2=961%2F12 ALIGN=MIDDLE  ALT=\"3%28w%2B1%2F6%29%5E2=961%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28w%2B1%2F6%29%5E2=961%2F36 ALIGN=MIDDLE  ALT=\"%28w%2B1%2F6%29%5E2=961%2F36\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w%2B1%2F6=0%2B-+sqrt%28961%2F36%29 ALIGN=MIDDLE  ALT=\"w%2B1%2F6=0%2B-+sqrt%28961%2F36%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w=-1%2F6%2B-+31%2F6 ALIGN=MIDDLE  ALT=\"w=-1%2F6%2B-+31%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w=%28-1-31%29%2F6 ALIGN=MIDDLE  ALT=\"w=%28-1-31%29%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > OR <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w=%28-1%2B31%29%2F6 ALIGN=MIDDLE  ALT=\"w=%28-1%2B31%29%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cross%28w=-32%2F6%29 ALIGN=MIDDLE  ALT=\"cross%28w=-32%2F6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >  OR  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28w=5%29 ALIGN=MIDDLE  ALT=\"highlight%28w=5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The meaningful result here is w=5 for width.\r<BR>\n" );
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document.write( "You could have found 5 and 16 for your attempt at factorization of the general quadratic in w.<BR>\n" );
document.write( "That seemed like something which would take too many different trys to find.\r<BR>\n" );
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document.write( "Now, you can just use the formula for L and the now known value for w.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=3w%2B1 ALIGN=MIDDLE  ALT=\"L=3w%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=3%2A5%2B1 ALIGN=MIDDLE  ALT=\"L=3%2A5%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28L=16%29 ALIGN=MIDDLE  ALT=\"highlight%28L=16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Also, once getting the earlier simpler quadratic in w, the general solution could have been chosen:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3w%5E2%2Bw-80=0 ALIGN=MIDDLE  ALT=\"3w%5E2%2Bw-80=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >;<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w=%28-1%2B-+sqrt%281-4%2A3%2A%28-80%29%29%29%2F%282%2A3%29 ALIGN=MIDDLE  ALT=\"w=%28-1%2B-+sqrt%281-4%2A3%2A%28-80%29%29%29%2F%282%2A3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and then evaluate (and choose the value which makes sense.)<BR>\n" );
document.write( " </SPAN>\n" );
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