document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=130296>Question 130296</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Looking at <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f%28x%29=-0.2x%5E2%2B12x%2B11 ALIGN=MIDDLE  ALT=\"f%28x%29=-0.2x%5E2%2B12x%2B11\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Use the quadratic equation to determine the last day that tickets will be sold. (Note: Write your answer in terms of the number of days after ticket sales begin.) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #95157 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=95157\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The last day of ticket sales will correspond to the rightmost zero. So we need to find the zeros\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=-0.2x%5E2%2B12x%2B11 ALIGN=MIDDLE  ALT=\"y=-0.2x%5E2%2B12x%2B11\"   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=0=-0.2x%5E2%2B12x%2B11 ALIGN=MIDDLE  ALT=\"0=-0.2x%5E2%2B12x%2B11\"   DISABLED_style= \"max-width:90%; height:auto;\" > Set y equal to zero\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%280%29=10%28-0.2x%5E2%2B12x%2B11%29 ALIGN=MIDDLE  ALT=\"10%280%29=10%28-0.2x%5E2%2B12x%2B11%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply both sides by 10 to get rid of the decimal number\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=-2x%5E2%2B120x%2B110 ALIGN=MIDDLE  ALT=\"0=-2x%5E2%2B120x%2B110\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute and multiply \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=-2%2Ax%5E2%2B120%2Ax%2B110=0 ALIGN=MIDDLE  ALT=\"-2%2Ax%5E2%2B120%2Ax%2B110=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( notice <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=-2 ALIGN=MIDDLE  ALT=\"a=-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=120 ALIGN=MIDDLE  ALT=\"b=120\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=110 ALIGN=MIDDLE  ALT=\"c=110\"   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+=+%28-120+%2B-+sqrt%28+%28120%29%5E2-4%2A-2%2A110+%29%29%2F%282%2A-2%29 ALIGN=MIDDLE  ALT=\"x+=+%28-120+%2B-+sqrt%28+%28120%29%5E2-4%2A-2%2A110+%29%29%2F%282%2A-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in a=-2, b=120, and c=110\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-120+%2B-+sqrt%28+14400-4%2A-2%2A110+%29%29%2F%282%2A-2%29 ALIGN=MIDDLE  ALT=\"x+=+%28-120+%2B-+sqrt%28+14400-4%2A-2%2A110+%29%29%2F%282%2A-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square 120 to get 14400  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-120+%2B-+sqrt%28+14400%2B880+%29%29%2F%282%2A-2%29 ALIGN=MIDDLE  ALT=\"x+=+%28-120+%2B-+sqrt%28+14400%2B880+%29%29%2F%282%2A-2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%2A110%2A-2 ALIGN=MIDDLE  ALT=\"-4%2A110%2A-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=880 ALIGN=MIDDLE  ALT=\"880\"   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+=+%28-120+%2B-+sqrt%28+15280+%29%29%2F%282%2A-2%29 ALIGN=MIDDLE  ALT=\"x+=+%28-120+%2B-+sqrt%28+15280+%29%29%2F%282%2A-2%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+=+%28-120+%2B-+4%2Asqrt%28955%29%29%2F%282%2A-2%29 ALIGN=MIDDLE  ALT=\"x+=+%28-120+%2B-+4%2Asqrt%28955%29%29%2F%282%2A-2%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+=+%28-120+%2B-+4%2Asqrt%28955%29%29%2F-4 ALIGN=MIDDLE  ALT=\"x+=+%28-120+%2B-+4%2Asqrt%28955%29%29%2F-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 2 and -2 to get -4\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( "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=-120%2F-4%2B4%2Asqrt%28955%29%2F-4 ALIGN=MIDDLE  ALT=\"x=-120%2F-4%2B4%2Asqrt%28955%29%2F-4\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-120%2F-4-4%2Asqrt%28955%29%2F-4 ALIGN=MIDDLE  ALT=\"x=-120%2F-4-4%2Asqrt%28955%29%2F-4\"   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( "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=-0.903074280724887 ALIGN=MIDDLE  ALT=\"x=-0.903074280724887\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=60.9030742807249 ALIGN=MIDDLE  ALT=\"x=60.9030742807249\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So our solutions are:\r<BR>\n" );
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document.write( "So the last day of ticket sales will be on the 60th day </SPAN>\n" );
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