document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=200644>Question 200644</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find x if shaded area of a rectangle is 90(the whole rectangle is shaded except for the 3 holes). By developing and solving by factoring quadratic equation. The rectangle width is 2x-2, length is 3x, and there are 3 holes cut out with the width of x and length of x-1. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #151098 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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=151098\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> I don't have a diagram of this situation but we can muddle through without one.<BR>\n" );
document.write( "First, the big rectangle has an area of:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5B1%5D+=+%282x-2%29%283x%29 ALIGN=MIDDLE  ALT=\"A%5B1%5D+=+%282x-2%29%283x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5B1%5D+=+6x%5E2-6x ALIGN=MIDDLE  ALT=\"A%5B1%5D+=+6x%5E2-6x\"   DISABLED_style= \"max-width:90%; height:auto;\" > now we'll subtract the area of the three (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%28x%2A%28x-1%29%29 ALIGN=MIDDLE  ALT=\"3%28x%2A%28x-1%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >) rectangular holes whose total area is: <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5B2%5D+=+3x%5E2-3x ALIGN=MIDDLE  ALT=\"A%5B2%5D+=+3x%5E2-3x\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5B1%5D-A%5B2%5D+=+6x%5E2-6x-%283x%5E2-3x%29 ALIGN=MIDDLE  ALT=\"A%5B1%5D-A%5B2%5D+=+6x%5E2-6x-%283x%5E2-3x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Bt%5D+=+3x%5E2-3x ALIGN=MIDDLE  ALT=\"A%5Bt%5D+=+3x%5E2-3x\"   DISABLED_style= \"max-width:90%; height:auto;\" > and this, the problem tells us is 90, so...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2-3x+=+90 ALIGN=MIDDLE  ALT=\"3x%5E2-3x+=+90\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 90 from both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2-3x-90+=+0 ALIGN=MIDDLE  ALT=\"3x%5E2-3x-90+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor out a 3 to facilitate the calculation.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%28x%5E2-x-30%29+=+0 ALIGN=MIDDLE  ALT=\"3%28x%5E2-x-30%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > which means that...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-x-30+=+0 ALIGN=MIDDLE  ALT=\"x%5E2-x-30+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor this quadratic equation.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B5%29%28x-6%29+=+0 ALIGN=MIDDLE  ALT=\"%28x%2B5%29%28x-6%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > so...<BR>\n" );
document.write( "<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;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28x+=+6%29 ALIGN=MIDDLE  ALT=\"highlight_green%28x+=+6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Discard the negative solution as the length, x, can only be positive. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );