document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=251684>Question 251684</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Problem: Originally, a rectangle was three times as long as it is wide. When 2 cm were subtracted from the length and 5 cm were added to the width, the resulting rectangle had an area of 90 cm squared. Find the dimensions of the new rectangle.\r<BR>\n" );
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document.write( "hmmmm, I tried this problem...but I keep getting decimal answers when solving :/ We are supposed to use only one variable in the actual equation, and use Quadratic equations to solve. \r<BR>\n" );
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document.write( "My Attempt:\r<BR>\n" );
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document.write( "w=width<BR>\n" );
document.write( "l=length<BR>\n" );
document.write( "l=3w\r<BR>\n" );
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document.write( "Formula-<BR>\n" );
document.write( "A=width(length)<BR>\n" );
document.write( "(3w-2)(w+5)=90<BR>\n" );
document.write( "Then I foiled and got:<BR>\n" );
document.write( "3w^2+13w-100=0<BR>\n" );
document.write( "And I get stuck there :/ I don't think it factors and I'm not sure if I foiled wrong or set it up wrong. :/ Help me, please? Thanks :)\r<BR>\n" );
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document.write( "I put this under Algebra, although I am in Algebra II, I hope that is fine :D </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #183356 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3758)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><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=183356\">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=%283w-2%29%28w%2B5%29=90 ALIGN=MIDDLE  ALT=\"%283w-2%29%28w%2B5%29=90\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then I foiled and got:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3w%5E2%2B13w-100=0 ALIGN=MIDDLE  ALT=\"3w%5E2%2B13w-100=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "And I get stuck there :/ I don't think it factors and I'm not sure if I foiled wrong or set it up wrong. :/ Help me, please? Thanks :)<BR>\n" );
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document.write( "This is all good. If you think this trinomial does not factor, then use the quadratic formula on it. (This trinomial actually does factor but the quadratic formula still works.)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w+=+%28-b+%2B-+sqrt%28b%5E2+-+4ac%29%29%2F2a ALIGN=MIDDLE  ALT=\"w+=+%28-b+%2B-+sqrt%28b%5E2+-+4ac%29%29%2F2a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Your a = 3, b = 13 and c = -100:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w+=+%28-%2813%29+%2B-+sqrt%28%2813%29%5E2+-+4%283%29%28-100%29%29%29%2F2%283%29 ALIGN=MIDDLE  ALT=\"w+=+%28-%2813%29+%2B-+sqrt%28%2813%29%5E2+-+4%283%29%28-100%29%29%29%2F2%283%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+=+%28-13+%2B-+sqrt%28169+-+4%283%29%28-100%29%29%29%2F6 ALIGN=MIDDLE  ALT=\"w+=+%28-13+%2B-+sqrt%28169+-+4%283%29%28-100%29%29%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=w+=+%28-13+%2B-+sqrt%28169+%2B+1200%29%29%2F6 ALIGN=MIDDLE  ALT=\"w+=+%28-13+%2B-+sqrt%28169+%2B+1200%29%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=w+=+%28-13+%2B-+sqrt%281369%29%29%2F6 ALIGN=MIDDLE  ALT=\"w+=+%28-13+%2B-+sqrt%281369%29%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=w+=+%28-13+%2B-+37%29%2F6 ALIGN=MIDDLE  ALT=\"w+=+%28-13+%2B-+37%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=w+=+%28-13+%2B+37%29%2F6 ALIGN=MIDDLE  ALT=\"w+=+%28-13+%2B+37%29%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w+=+%28-13+-+37%29%2F6 ALIGN=MIDDLE  ALT=\"w+=+%28-13+-+37%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=w+=+24%2F6 ALIGN=MIDDLE  ALT=\"w+=+24%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w+=+%28-50%29%2F6 ALIGN=MIDDLE  ALT=\"w+=+%28-50%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=w+=+4 ALIGN=MIDDLE  ALT=\"w+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w+=+%28-25%29%2F3 ALIGN=MIDDLE  ALT=\"w+=+%28-25%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Since w represents the side of a rectangle we will reject the negative solution. So the only possible value for w that works is w = 4. And that makes the original length, which is 3w, 12.<br><BR>\n" );
document.write( "BTW: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3w%5E2%2B13w-100=0 ALIGN=MIDDLE  ALT=\"3w%5E2%2B13w-100=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > factors into:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283w+%2B+25%29%28w+-+4%29+=+0 ALIGN=MIDDLE  ALT=\"%283w+%2B+25%29%28w+-+4%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "And this gives us the same answers as the quadratic formula did. </SPAN>\n" );
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