document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=385217>Question 385217</A>: <I><SPAN STYLE=\"word-break: break-all;\"> i'm learning polynomials and such in class and a question came up in one of my group tests. i asked someone else for help and they showed me how to do it but i don't get how to get from the equation to the answer.\r<BR>\n" );
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document.write( "i do not understand how 2w^2+11w=84 gets to whatever the weird answer was. i do not understand how it is a quadratic equation and how to simplify it...please help and thanks so much.\r<BR>\n" );
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document.write( "PS. the problem i had on my group test was this:<BR>\n" );
document.write( "The length of a picture is one inch less than twice its width. the frame around the picture has a uniform width of two inches and an area of 96 square inches. what are the dimensions of the picture?<BR>\n" );
document.write( "i did the equation like this:<BR>\n" );
document.write( "(2w+3)(w+4)=96<BR>\n" );
document.write( "which simplified to:<BR>\n" );
document.write( "2w^2+11w=84  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #272554 by </B><A HREF=/tutors/aboutme.mpl?userid=mananth><B>mananth(16946)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mananth><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=mananth><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=272554\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The length of a picture is one inch less than twice its width. the frame around the picture has a uniform width of two inches and an area of 96 square inches. what are the dimensions of the picture?<BR>\n" );
document.write( "...<BR>\n" );
document.write( "width of picture = w<BR>\n" );
document.write( "length = 2w-1<BR>\n" );
document.write( "...<BR>\n" );
document.write( "Area of picture = w(2w-1)<BR>\n" );
document.write( "...<BR>\n" );
document.write( "uniform width of 2 in.surrounding the picture<BR>\n" );
document.write( "so width will be w+4<BR>\n" );
document.write( "length = (2w-1)+4=2w+3<BR>\n" );
document.write( "..<BR>\n" );
document.write( "Area of picture + area frame =(w+4)(2w+3)<BR>\n" );
document.write( "...<BR>\n" );
document.write( "(Area of picture + area frame)-area of picture= area of frame<BR>\n" );
document.write( "..<BR>\n" );
document.write( "(w+3)(2w+3)-w(2w-1)=96<BR>\n" );
document.write( "2w^2+9w+9-2w^2+w=96<BR>\n" );
document.write( "10w+9=96<BR>\n" );
document.write( "-9   -9<BR>\n" );
document.write( "10w=87<BR>\n" );
document.write( "/10<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28highlight%28w=8.7%29%29 ALIGN=MIDDLE  ALT=\"%28highlight%28w=8.7%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >cm the width<BR>\n" );
document.write( "Length = 2w-1= 2*8.7-1<BR>\n" );
document.write( "Length =17.4-1<BR>\n" );
document.write( "Length<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28highlight%28l=16.4%29%29 ALIGN=MIDDLE  ALT=\"%28highlight%28l=16.4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >cm </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );