document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=833912>Question 833912</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Help! Don't know how to put story problem into quadratic formula:\r<BR>\n" );
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document.write( "A rectangular garden is 30 ft by 40 ft. Part of the garden is removed in order to install a walkway of uniform width around it. The area of the new garden is one-half the area of the old garden. 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 #502756 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=502756\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A rectangular garden is 30 ft by 40 ft. Part of the garden is removed in order to install a walkway of uniform width around it. The area of the new garden is one-half the area of the old garden. How wide is the walkway?\r<BR>\n" );
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document.write( "Area of the entire garden is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=+30ft+%2A+40ft+=+1200ft%5E2 ALIGN=MIDDLE  ALT=\"A=+30ft+%2A+40ft+=+1200ft%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > be the width of the walkway.\r<BR>\n" );
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document.write( "Length of the reduced garden is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=+%2840+-+2x%29ft ALIGN=MIDDLE  ALT=\"L=+%2840+-+2x%29ft\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Width of the reduced garden is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+W=+%2830+-+2x%29ft ALIGN=MIDDLE  ALT=\"+W=+%2830+-+2x%29ft\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Area of the reduced garden is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Br%5D+=+%2840+-+2x%29+%2A+%2830+-+2x%29ft%5E2 ALIGN=MIDDLE  ALT=\"A%5Br%5D+=+%2840+-+2x%29+%2A+%2830+-+2x%29ft%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Area of the reduced garden is one-half the area of the old garden; so, we have<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Br%5D+=A%2F2 ALIGN=MIDDLE  ALT=\"A%5Br%5D+=A%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2A%5Br%5D+=A ALIGN=MIDDLE  ALT=\"2A%5Br%5D+=A\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "since<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5Br%5D+=+%2840+-+2x%29+%2A+%2830+-+2x%29ft%5E2 ALIGN=MIDDLE  ALT=\"A%5Br%5D+=+%2840+-+2x%29+%2A+%2830+-+2x%29ft%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=+1200ft%5E2 ALIGN=MIDDLE  ALT=\"A=+1200ft%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, we have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2840+-+2x%29+%2A+%2830+-+2x%29ft%5E2=1200ft%5E2 ALIGN=MIDDLE  ALT=\"2%2840+-+2x%29+%2A+%2830+-+2x%29ft%5E2=1200ft%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >...simplify\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2840+-+2x%29+%2A+%2830+-+2x%29=600 ALIGN=MIDDLE  ALT=\"%2840+-+2x%29+%2A+%2830+-+2x%29=600\"   DISABLED_style= \"max-width:90%; height:auto;\" >....expand\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=120+-80x-+60x+%2B+4x%5E2=600 ALIGN=MIDDLE  ALT=\"120+-80x-+60x+%2B+4x%5E2=600\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4x%5E2-140x%2B1200=600 ALIGN=MIDDLE  ALT=\"+4x%5E2-140x%2B1200=600\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4x%5E2-140x%2B1200-600=0 ALIGN=MIDDLE  ALT=\"+4x%5E2-140x%2B1200-600=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4x%5E2-140x-600=0 ALIGN=MIDDLE  ALT=\"+4x%5E2-140x-600=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >...both sides divide by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4 ALIGN=MIDDLE  ALT=\"4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5E2-35x-150=0 ALIGN=MIDDLE  ALT=\"+x%5E2-35x-150=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >......solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >\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_formula.solver>Quadratic Formula</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Let's use the quadratic formula to solve for x:<BR><BR>\n" );
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document.write( "  Starting with the general quadratic<BR>\n" );
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document.write( "  <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;\" ><BR>\n" );
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document.write( "  the general solution using the quadratic equation is:<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29 ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  So lets solve <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2Ax%5E2-140%2Ax%2B600=0 ALIGN=MIDDLE  ALT=\"4%2Ax%5E2-140%2Ax%2B600=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( notice <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=4 ALIGN=MIDDLE  ALT=\"a=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=-140 ALIGN=MIDDLE  ALT=\"b=-140\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=600 ALIGN=MIDDLE  ALT=\"c=600\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28--140+%2B-+sqrt%28+%28-140%29%5E2-4%2A4%2A600+%29%29%2F%282%2A4%29 ALIGN=MIDDLE  ALT=\"x+=+%28--140+%2B-+sqrt%28+%28-140%29%5E2-4%2A4%2A600+%29%29%2F%282%2A4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in a=4, b=-140, and c=600<BR>\n" );
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document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28140+%2B-+sqrt%28+%28-140%29%5E2-4%2A4%2A600+%29%29%2F%282%2A4%29 ALIGN=MIDDLE  ALT=\"x+=+%28140+%2B-+sqrt%28+%28-140%29%5E2-4%2A4%2A600+%29%29%2F%282%2A4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Negate -140 to get 140<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28140+%2B-+sqrt%28+19600-4%2A4%2A600+%29%29%2F%282%2A4%29 ALIGN=MIDDLE  ALT=\"x+=+%28140+%2B-+sqrt%28+19600-4%2A4%2A600+%29%29%2F%282%2A4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square -140 to get 19600  (note: remember when you square -140, you must square the negative as well. This is because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-140%29%5E2=-140%2A-140=19600 ALIGN=MIDDLE  ALT=\"%28-140%29%5E2=-140%2A-140=19600\"   DISABLED_style= \"max-width:90%; height:auto;\" >.)<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28140+%2B-+sqrt%28+19600%2B-9600+%29%29%2F%282%2A4%29 ALIGN=MIDDLE  ALT=\"x+=+%28140+%2B-+sqrt%28+19600%2B-9600+%29%29%2F%282%2A4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%2A600%2A4 ALIGN=MIDDLE  ALT=\"-4%2A600%2A4\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-9600 ALIGN=MIDDLE  ALT=\"-9600\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  <BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28140+%2B-+sqrt%28+10000+%29%29%2F%282%2A4%29 ALIGN=MIDDLE  ALT=\"x+=+%28140+%2B-+sqrt%28+10000+%29%29%2F%282%2A4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms in the radicand (everything under the square root)<BR>\n" );
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document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28140+%2B-+100%29%2F%282%2A4%29 ALIGN=MIDDLE  ALT=\"x+=+%28140+%2B-+100%29%2F%282%2A4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify the square root (note: If you need help with simplifying the square root, check out this <a  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Radicals/simplifying-square-roots.solver> solver</a>)<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28140+%2B-+100%29%2F8 ALIGN=MIDDLE  ALT=\"x+=+%28140+%2B-+100%29%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 2 and 4 to get 8<BR>\n" );
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document.write( "  So now the expression breaks down into two parts<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28140+%2B+100%29%2F8 ALIGN=MIDDLE  ALT=\"x+=+%28140+%2B+100%29%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28140+-+100%29%2F8 ALIGN=MIDDLE  ALT=\"x+=+%28140+-+100%29%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  Lets look at the first part:<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28140+%2B+100%29%2F8 ALIGN=MIDDLE  ALT=\"x=%28140+%2B+100%29%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=240%2F8 ALIGN=MIDDLE  ALT=\"x=240%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add the terms in the numerator<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=30 ALIGN=MIDDLE  ALT=\"x=30\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide<BR>\n" );
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document.write( "  So one answer is<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=30 ALIGN=MIDDLE  ALT=\"x=30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  Now lets look at the second part:<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28140+-+100%29%2F8 ALIGN=MIDDLE  ALT=\"x=%28140+-+100%29%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=40%2F8 ALIGN=MIDDLE  ALT=\"x=40%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract the terms in the numerator<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=5 ALIGN=MIDDLE  ALT=\"x=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide<BR>\n" );
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document.write( "  So another answer is<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=5 ALIGN=MIDDLE  ALT=\"x=5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  So our solutions are:<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=30 ALIGN=MIDDLE  ALT=\"x=30\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=5 ALIGN=MIDDLE  ALT=\"x=5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  </TD></TR>\n" );
document.write( "</TABLE>\n" );
document.write( " \r<BR>\n" );
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document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+5 ALIGN=MIDDLE  ALT=\"x+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the length is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=+%2840+-+2%2A5%29+=40-+10=30 ALIGN=MIDDLE  ALT=\"L=+%2840+-+2%2A5%29+=40-+10=30\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "and width <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W=+%2830+-+2%2A5%29+=30-10=20 ALIGN=MIDDLE  ALT=\"W=+%2830+-+2%2A5%29+=30-10=20\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+30 ALIGN=MIDDLE  ALT=\"x+=+30\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the length is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=+%2840+-+2%2A30%29+=40-+60=-20 ALIGN=MIDDLE  ALT=\"L=+%2840+-+2%2A30%29+=40-+60=-20\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "and width <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=W=+%2830+-+2%2A30%29+=+-30 ALIGN=MIDDLE  ALT=\"W=+%2830+-+2%2A30%29+=+-30\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So, the second case (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+30 ALIGN=MIDDLE  ALT=\"x+=+30\"   DISABLED_style= \"max-width:90%; height:auto;\" >) is ruled out because you can't have a width and a length equal to negative number.\r<BR>\n" );
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document.write( "so the walkway is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=5ft ALIGN=MIDDLE  ALT=\"x=5ft\"   DISABLED_style= \"max-width:90%; height:auto;\" > wide<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );