document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=762397>Question 762397</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A gardener has a 30 foot by 20 foot rectangular plot of ground. she wants to build a brickway of uniform width on the border of the plot. if the gardener wants to have 400 square feet of ground left for planting, how wide (to two decimal places) should she build the walkway?\r<BR>\n" );
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document.write( "I solved 2.19 but it was using trial and error.<BR>\n" );
document.write( "my teacher asked for the complete process.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #463940 by </B><A HREF=/tutors/aboutme.mpl?userid=Stitch><B>Stitch(470)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Stitch><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=463940\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Area = length x width.<BR>\n" );
document.write( "If you are have a uniform walkway, then you have to subtract that distance from both sides of the length and width.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=400+=+%2830-2X%29%2A%2820-2X%29 ALIGN=MIDDLE  ALT=\"400+=+%2830-2X%29%2A%2820-2X%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Use FOIL to simplify the right hand side of the equation.<BR>\n" );
document.write( "ERROR Algebra::Solver::Engine::invoke_solver_noengine: solver not defined for name 'foil'.\n" );
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document.write( " <TR><TD >Error occurred executing solver 'foil' .</TD></TR>\n" );
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document.write( "Rewrite the equation.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=400+=+-100X+%2B+4X%5E2+%2B+600 ALIGN=MIDDLE  ALT=\"400+=+-100X+%2B+4X%5E2+%2B+600\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Subtract 400 from both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+4X%5E2+-+100X+%2B+200 ALIGN=MIDDLE  ALT=\"0+=+4X%5E2+-+100X+%2B+200\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now use the quadratic equation to solve for X.<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%2B-100X%2B200+=+0 ALIGN=MIDDLE  ALT=\"4X%5E2%2B-100X%2B200+=+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=%28-100%29%5E2-4%2A4%2A200=6800 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-100%29%5E2-4%2A4%2A200=6800\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=6800 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--100%2B-sqrt%28+6800+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--100%2B-sqrt%28+6800+%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-%28-100%29%2Bsqrt%28+6800+%29%29%2F2%5C4+=+22.8077640640442 ALIGN=MIDDLE  ALT=\"X%5B1%5D+=+%28-%28-100%29%2Bsqrt%28+6800+%29%29%2F2%5C4+=+22.8077640640442\"   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-%28-100%29-sqrt%28+6800+%29%29%2F2%5C4+=+2.19223593595585 ALIGN=MIDDLE  ALT=\"X%5B2%5D+=+%28-%28-100%29-sqrt%28+6800+%29%29%2F2%5C4+=+2.19223593595585\"   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%2B-100X%2B200 ALIGN=MIDDLE  ALT=\"4X%5E2%2B-100X%2B200\"   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%2B-100X%2B200+=+4%28X-22.8077640640442%29%2A%28X-2.19223593595585%29 ALIGN=MIDDLE  ALT=\"4X%5E2%2B-100X%2B200+=+4%28X-22.8077640640442%29%2A%28X-2.19223593595585%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 22.8077640640442, 2.19223593595585.\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%2B-100%2Ax%2B200+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B-100%2Ax%2B200+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "X = 2.19 & 22.81<BR>\n" );
document.write( "Now if you use 22.81 in the equation for the area of the garden you will come up with negative area. Since we can not have negative area 22.81 is not a real solution to this problem.<BR>\n" );
document.write( "X = 2.19feet\r<BR>\n" );
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