document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=610945>Question 610945</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I need help solving this problem\r<BR>\n" );
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document.write( "The length of a rectangular pool is 4 ft longer than the width. The area of the swimming pool measures 60 square ft. Find the dimensions of the pool. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #384678 by </B><A HREF=/tutors/aboutme.mpl?userid=radh><B>radh(108)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=radh><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=radh><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=384678\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's write this word problem mathematically and remove excess. First of all, we know that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=l%2Aw=a ALIGN=MIDDLE  ALT=\"l%2Aw=a\"   DISABLED_style= \"max-width:90%; height:auto;\" >. <BR>\n" );
document.write( "The length of a rectangular pool is 4 ft longer than width (w+4). The area (*, not adding) measures 60 square feet. \r<BR>\n" );
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document.write( "<p>To write this mathematically, it'd turn into: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28w%2B4%29%2A%28w%29=60 ALIGN=MIDDLE  ALT=\"%28w%2B4%29%2A%28w%29=60\"   DISABLED_style= \"max-width:90%; height:auto;\" >. We can simplify that: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=simplify_cartoon%28+%28w%2B4%29%2A%28w%29+%29 ALIGN=MIDDLE  ALT=\"simplify_cartoon%28+%28w%2B4%29%2A%28w%29+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<p>We'd then move the 60 to the other side to get: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w%5E2%2B4w-60=0 ALIGN=MIDDLE  ALT=\"w%5E2%2B4w-60=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Use the quadratic formula to get your solutions: <TABLE  BORDER=1>\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=solve_quadratic_equation.solver>SOLVE quadratic equation (work shown, graph etc)</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=1x%5E2%2B4x%2B-60+=+0 ALIGN=MIDDLE  ALT=\"1x%5E2%2B4x%2B-60+=+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" );
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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=%284%29%5E2-4%2A1%2A-60=256 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%284%29%5E2-4%2A1%2A-60=256\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=256 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+=+%28-4%2B-sqrt%28+256+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-4%2B-sqrt%28+256+%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-%284%29%2Bsqrt%28+256+%29%29%2F2%5C1+=+6 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%284%29%2Bsqrt%28+256+%29%29%2F2%5C1+=+6\"   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-%284%29-sqrt%28+256+%29%29%2F2%5C1+=+-10 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%284%29-sqrt%28+256+%29%29%2F2%5C1+=+-10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1x%5E2%2B4x%2B-60 ALIGN=MIDDLE  ALT=\"1x%5E2%2B4x%2B-60\"   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=1x%5E2%2B4x%2B-60+=+%28x-6%29%2A%28x--10%29 ALIGN=MIDDLE  ALT=\"1x%5E2%2B4x%2B-60+=+%28x-6%29%2A%28x--10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 6, -10.\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+1%2Ax%5E2%2B4%2Ax%2B-60+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B4%2Ax%2B-60+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( "Because there can't be a negative in getting a positive area, we'd assume x is 6. \r<BR>\n" );
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document.write( "<p>Let's go back into the normal equation to check the length and the width: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%286%2B4%29%2A%286%29=60 ALIGN=MIDDLE  ALT=\"%286%2B4%29%2A%286%29=60\"   DISABLED_style= \"max-width:90%; height:auto;\" >. It's correct, so we know that length is 10 and width is 6. :) </SPAN>\n" );
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