document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=902253>Question 902253</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A 22-ft by 28 ft rectangular swimming pool is surrounded by a walkway of uniform width. If the total area of the walkway is 216 ft^2, how wide is the walkway?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #547200 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=547200\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The area of a rectangle is given by the equation A = L*W, where L is the length and W is the width.<BR>\n" );
document.write( "We can find the total area of the larger rectangle (The area of the pool + the area of the walkway) by adding the two areas together.<BR>\n" );
document.write( "The area of the pool is :<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=22+%2A+28+=+616 ALIGN=MIDDLE  ALT=\"22+%2A+28+=+616\"   DISABLED_style= \"max-width:90%; height:auto;\" >ft^2<BR>\n" );
document.write( "Now we will added the two given areas together to find the total area of the pool and the walkway.<BR>\n" );
document.write( "616ft^2 + 216ft^2 = 832ft^2<BR>\n" );
document.write( "Now we need to write the equation of the area of the new large rectangle.<BR>\n" );
document.write( "Let X be the width of the walkway.<BR>\n" );
document.write( "The new length: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L+=+X+%2B+22+%2B+X ALIGN=MIDDLE  ALT=\"L+=+X+%2B+22+%2B+X\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The new width: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W+=+X+%2B+28+%2B+X ALIGN=MIDDLE  ALT=\"W+=+X+%2B+28+%2B+X\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The new area equation is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=832+=+%28X+%2B+22+%2B+X%29+%2A+%28X+%2B+28+%2B+X%29 ALIGN=MIDDLE  ALT=\"832+=+%28X+%2B+22+%2B+X%29+%2A+%28X+%2B+28+%2B+X%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Combine like terms<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=832+=+%282X+%2B+22%29+%2A+%282X+%2B+28%29 ALIGN=MIDDLE  ALT=\"832+=+%282X+%2B+22%29+%2A+%282X+%2B+28%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=832+=+4X%5E2+%2B+100X+%2B+616 ALIGN=MIDDLE  ALT=\"832+=+4X%5E2+%2B+100X+%2B+616\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Subtract 832 from both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+0+=+4X%5E2+%2B+100X+-+216 ALIGN=MIDDLE  ALT=\"+0+=+4X%5E2+%2B+100X+-+216\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now use the quadratic equation to solve for X.<BR>\n" );
document.write( "<TABLE  BORDER=1>\n" );
document.write( "\n" );
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%2B56X%2B-165+=+0 ALIGN=MIDDLE  ALT=\"4X%5E2%2B56X%2B-165+=+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=%2856%29%5E2-4%2A4%2A-165=5776 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%2856%29%5E2-4%2A4%2A-165=5776\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=5776 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+=+%28-56%2B-sqrt%28+5776+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-56%2B-sqrt%28+5776+%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-%2856%29%2Bsqrt%28+5776+%29%29%2F2%5C4+=+2.5 ALIGN=MIDDLE  ALT=\"X%5B1%5D+=+%28-%2856%29%2Bsqrt%28+5776+%29%29%2F2%5C4+=+2.5\"   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-%2856%29-sqrt%28+5776+%29%29%2F2%5C4+=+-16.5 ALIGN=MIDDLE  ALT=\"X%5B2%5D+=+%28-%2856%29-sqrt%28+5776+%29%29%2F2%5C4+=+-16.5\"   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%2B56X%2B-165 ALIGN=MIDDLE  ALT=\"4X%5E2%2B56X%2B-165\"   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%2B56X%2B-165+=+4%28X-2.5%29%2A%28X--16.5%29 ALIGN=MIDDLE  ALT=\"4X%5E2%2B56X%2B-165+=+4%28X-2.5%29%2A%28X--16.5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 2.5, -16.5.\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%2B56%2Ax%2B-165+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+4%2Ax%5E2%2B56%2Ax%2B-165+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "\n" );
document.write( "X = 2.5 & -16.5<BR>\n" );
document.write( "Now since we can not have a negative distance -16.5ft will not work for this problem.<BR>\n" );
document.write( "So the width of the walkway is 2.5ft </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );