document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=242913>Question 242913</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A concrete border of uniform width is constructed around a rectangular flower bed that is 12ft by 9 ft. Find the width of the border if the area formed by the flower bed and the border is 154 sq ft.\r<BR>\n" );
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document.write( "Can you help me solve this word problem. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #177898 by </B><A HREF=/tutors/aboutme.mpl?userid=JimboP1977><B>JimboP1977(311)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=JimboP1977><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=JimboP1977><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=177898\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Best thing to do with problems like this is to draw a diagram.\r<BR>\n" );
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document.write( "From the diagram you will see that the area between the border and the flower bed is equal to the 12 foot of the flower bed added to twice the width of the border multiplied by 9 plus twice the width of the bed.\r<BR>\n" );
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document.write( "Using Algebra, if x is the unknown width:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2812%2B2x%29%289%2B2x%29+=+154 ALIGN=MIDDLE  ALT=\"%2812%2B2x%29%289%2B2x%29+=+154\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2%2B24x%2B18x%2B108%29+=+154 ALIGN=MIDDLE  ALT=\"4x%5E2%2B24x%2B18x%2B108%29+=+154\"   DISABLED_style= \"max-width:90%; height:auto;\" >Multiply out<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2%2B42x%2B108%29+=+154 ALIGN=MIDDLE  ALT=\"4x%5E2%2B42x%2B108%29+=+154\"   DISABLED_style= \"max-width:90%; height:auto;\" >Collect terms<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2%2B42x-46%29+=+0 ALIGN=MIDDLE  ALT=\"4x%5E2%2B42x-46%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >Set to zero\r<BR>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=quadratic.solver>SOLVE quadratic equation with variable</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Quadratic equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc=0 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2%2B42x%2B-46+=+0 ALIGN=MIDDLE  ALT=\"4x%5E2%2B42x%2B-46+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) has the following solutons:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  For these solutions to exist, the <U>discriminant</U> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" > should not be a negative number.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  First, we need to compute the discriminant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" >: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac=%2842%29%5E2-4%2A4%2A-46=2500 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%2842%29%5E2-4%2A4%2A-46=2500\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=2500 is greater than zero. That means that there are two solutions: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5B12%5D+=+%28-42%2B-sqrt%28+2500+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-42%2B-sqrt%28+2500+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D+=+%28-%2842%29%2Bsqrt%28+2500+%29%29%2F2%5C4+=+1 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%2842%29%2Bsqrt%28+2500+%29%29%2F2%5C4+=+1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D+=+%28-%2842%29-sqrt%28+2500+%29%29%2F2%5C4+=+-11.5 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%2842%29-sqrt%28+2500+%29%29%2F2%5C4+=+-11.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <BR>\n" );
document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2%2B42x%2B-46 ALIGN=MIDDLE  ALT=\"4x%5E2%2B42x%2B-46\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be factored:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2%2B42x%2B-46+=+4%28x-1%29%2A%28x--11.5%29 ALIGN=MIDDLE  ALT=\"4x%5E2%2B42x%2B-46+=+4%28x-1%29%2A%28x--11.5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 1, -11.5.\n" );
document.write( "Here's your graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B42%2Ax%2B-46+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B42%2Ax%2B-46+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "So x must be positive so x is 1 ft\r<BR>\n" );
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