document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=122670>Question 122670</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A rectangular field is 200m by 300m.  A roadway of width xm is to be built just inside the field.  What is the widest the roadway can be and still leave 50,000m^2 in the region?\r<BR>\n" );
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document.write( "60,000 - 400x - 600x +x = 50,000\r<BR>\n" );
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document.write( "Am I on the right track for solving the problem with this formula? I feel like I'm missing something.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #90062 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=90062\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First let's draw a picture. We can see that the length of the inner rectangle is  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=300-2x ALIGN=MIDDLE  ALT=\"300-2x\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the width of the inner rectangle is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=200-2x ALIGN=MIDDLE  ALT=\"200-2x\"   DISABLED_style= \"max-width:90%; height:auto;\" > since we are taking away <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x ALIGN=MIDDLE  ALT=\"2x\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both the length and the width.\r<BR>\n" );
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document.write( "note: the inner rectangle represents the remaining area\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28500%2C500%2C-10%2C7%2C-7%2C7%2C%0D%0Ablue%28line%28-5%2C3%2C5%2C3%29%29%2C%0D%0Ablue%28line%285%2C3%2C5%2C-3%29%29%2C%0D%0Ablue%28line%285%2C-3%2C-5%2C-3%29%29%2C%0D%0Ablue%28line%28-5%2C-3%2C-5%2C3%29%29%2C%0D%0Ared%28line%28-6%2C4%2C6%2C4%29%29%2C%0D%0Ared%28line%286%2C4%2C6%2C-4%29%29%2C%0D%0Ared%28line%286%2C-4%2C-6%2C-4%29%29%2C%0D%0Ared%28line%28-6%2C-4%2C-6%2C4%29%29%2C%0D%0Agreen%28line%28-5%2C3%2C-5%2C4%29%29%2C%0D%0Agreen%28line%28-5%2C3%2C-6%2C3%29%29%2C%0D%0Agreen%28line%285%2C3%2C5%2C4%29%29%2C%0D%0Agreen%28line%285%2C3%2C6%2C3%29%29%2C%0D%0Agreen%28line%28-5%2C-3%2C-5%2C-4%29%29%2C%0D%0Agreen%28line%28-5%2C-3%2C-6%2C-3%29%29%2C%0D%0Agreen%28line%285%2C-3%2C6%2C-3%29%29%2C%0D%0Agreen%28line%285%2C-3%2C5%2C-4%29%29%2C%0D%0Ared%28locate%28-0.5%2C4.5%2CLength%3A300%29%29%2C%0D%0Ablue%28locate%28-0.5%2C3.5%2CLength%3A300-2x%29%29%2C%0D%0Ared%28locate%28-8%2C0%2CWidth%3A200%29%29%2C%0D%0Ablue%28locate%28-7.95%2C1.2%2CWidth%3A200-2x%29%29%2C%0D%0Agreen%28locate%28-4.8%2C3.8%2Cx%29%29%2C%0D%0Agreen%28locate%28-5.6%2C3%2Cx%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "From the drawing, the area of remaining area is (ie the blue rectangle):\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=%28300-2x%29%28200-2x%29 ALIGN=MIDDLE  ALT=\"A=%28300-2x%29%28200-2x%29\"   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=A=%28300-2x%29%28200-2x%29 ALIGN=MIDDLE  ALT=\"A=%28300-2x%29%28200-2x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the given equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=50000=%28300-2x%29%28200-2x%29 ALIGN=MIDDLE  ALT=\"50000=%28300-2x%29%28200-2x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in A=50,000\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=50000=4x%5E2-1000x%2B60000 ALIGN=MIDDLE  ALT=\"50000=4x%5E2-1000x%2B60000\"   DISABLED_style= \"max-width:90%; height:auto;\" > Foil\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=4x%5E2-1000x%2B60000-50000 ALIGN=MIDDLE  ALT=\"0=4x%5E2-1000x%2B60000-50000\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 50,000 from both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=4x%5E2-1000x%2B10000 ALIGN=MIDDLE  ALT=\"0=4x%5E2-1000x%2B10000\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms\r<BR>\n" );
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document.write( "Let's use the quadratic formula to solve for x:\r<BR>\n" );
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document.write( "Starting with the general quadratic\r<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;\" >\r<BR>\n" );
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document.write( "the general solution using the quadratic equation is:\r<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;\" >\r<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%5E2-1000%2Ax%2B10000=0 ALIGN=MIDDLE  ALT=\"4%2Ax%5E2-1000%2Ax%2B10000=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=-1000 ALIGN=MIDDLE  ALT=\"b=-1000\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=10000 ALIGN=MIDDLE  ALT=\"c=10000\"   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+=+%28--1000+%2B-+sqrt%28+%28-1000%29%5E2-4%2A4%2A10000+%29%29%2F%282%2A4%29 ALIGN=MIDDLE  ALT=\"x+=+%28--1000+%2B-+sqrt%28+%28-1000%29%5E2-4%2A4%2A10000+%29%29%2F%282%2A4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in a=4, b=-1000, and c=10000\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%281000+%2B-+sqrt%28+%28-1000%29%5E2-4%2A4%2A10000+%29%29%2F%282%2A4%29 ALIGN=MIDDLE  ALT=\"x+=+%281000+%2B-+sqrt%28+%28-1000%29%5E2-4%2A4%2A10000+%29%29%2F%282%2A4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Negate -1000 to get 1000\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%281000+%2B-+sqrt%28+1000000-4%2A4%2A10000+%29%29%2F%282%2A4%29 ALIGN=MIDDLE  ALT=\"x+=+%281000+%2B-+sqrt%28+1000000-4%2A4%2A10000+%29%29%2F%282%2A4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square -1000 to get 1000000  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%281000+%2B-+sqrt%28+1000000%2B-160000+%29%29%2F%282%2A4%29 ALIGN=MIDDLE  ALT=\"x+=+%281000+%2B-+sqrt%28+1000000%2B-160000+%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%2A10000%2A4 ALIGN=MIDDLE  ALT=\"-4%2A10000%2A4\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-160000 ALIGN=MIDDLE  ALT=\"-160000\"   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+=+%281000+%2B-+sqrt%28+840000+%29%29%2F%282%2A4%29 ALIGN=MIDDLE  ALT=\"x+=+%281000+%2B-+sqrt%28+840000+%29%29%2F%282%2A4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms in the radicand (everything under the square root)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%281000+%2B-+200%2Asqrt%2821%29%29%2F%282%2A4%29 ALIGN=MIDDLE  ALT=\"x+=+%281000+%2B-+200%2Asqrt%2821%29%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>)\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%281000+%2B-+200%2Asqrt%2821%29%29%2F8 ALIGN=MIDDLE  ALT=\"x+=+%281000+%2B-+200%2Asqrt%2821%29%29%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 2 and 4 to get 8\r<BR>\n" );
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document.write( "So now the expression breaks down into two parts\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%281000+%2B+200%2Asqrt%2821%29%29%2F8 ALIGN=MIDDLE  ALT=\"x+=+%281000+%2B+200%2Asqrt%2821%29%29%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%281000+-+200%2Asqrt%2821%29%29%2F8 ALIGN=MIDDLE  ALT=\"x+=+%281000+-+200%2Asqrt%2821%29%29%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now break up the fraction\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%2B1000%2F8%2B200%2Asqrt%2821%29%2F8 ALIGN=MIDDLE  ALT=\"x=%2B1000%2F8%2B200%2Asqrt%2821%29%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%2B1000%2F8-200%2Asqrt%2821%29%2F8 ALIGN=MIDDLE  ALT=\"x=%2B1000%2F8-200%2Asqrt%2821%29%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Simplify\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=125%2B25%2Asqrt%2821%29 ALIGN=MIDDLE  ALT=\"x=125%2B25%2Asqrt%2821%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=125-25%2Asqrt%2821%29 ALIGN=MIDDLE  ALT=\"x=125-25%2Asqrt%2821%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So these expressions approximate to\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=239.564392373896 ALIGN=MIDDLE  ALT=\"x=239.564392373896\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=10.435607626104 ALIGN=MIDDLE  ALT=\"x=10.435607626104\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So our possible solutions are:\r<BR>\n" );
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document.write( "However, if you plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=239.564392373896 ALIGN=MIDDLE  ALT=\"x=239.564392373896\"   DISABLED_style= \"max-width:90%; height:auto;\" > into <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=%28300-2x%29%28200-2x%29 ALIGN=MIDDLE  ALT=\"A=%28300-2x%29%28200-2x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > , it will give you a negative area, so our only solution is \r<BR>\n" );
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document.write( "So the roadway can be about 10.44 m wide which will leave 50,000 m^2 of field\r<BR>\n" );
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document.write( " </SPAN>\n" );
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