document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=102615>Question 102615</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The demand and supply equations for a certain item are given by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D=-5p%2B40 ALIGN=MIDDLE  ALT=\"D=-5p%2B40\"   DISABLED_style= \"max-width:90%; height:auto;\" >  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S=-p%5E2%2B30p-8 ALIGN=MIDDLE  ALT=\"S=-p%5E2%2B30p-8\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now find the equilibrium price.<BR>\n" );
document.write( "Could someone please help me i am lost?<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #74643 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=74643\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To find the equilibrium price, set the two equations equal to one another\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-5p%2B40=-p%5E2%2B30p-8+ ALIGN=MIDDLE  ALT=\"-5p%2B40=-p%5E2%2B30p-8+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cross%28-5p%2B5p%2B40-40%29=-p%5E2%2B30p-8+%2B5p-40 ALIGN=MIDDLE  ALT=\"cross%28-5p%2B5p%2B40-40%29=-p%5E2%2B30p-8+%2B5p-40\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add 5p and subtract 40 from both sides to get everything to one side\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=-p%5E2%2B35p-48 ALIGN=MIDDLE  ALT=\"0=-p%5E2%2B35p-48\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Let's use the quadratic formula to solve for p:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Starting with the general quadratic\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ap%5E2%2Bbp%2Bc=0 ALIGN=MIDDLE  ALT=\"ap%5E2%2Bbp%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the general solution using the quadratic equation is:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29 ALIGN=MIDDLE  ALT=\"p+=+%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" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So lets solve <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-p%5E2%2B35%2Ap-48=0 ALIGN=MIDDLE  ALT=\"-p%5E2%2B35%2Ap-48=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( notice <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=-1 ALIGN=MIDDLE  ALT=\"a=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=35 ALIGN=MIDDLE  ALT=\"b=35\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=-48 ALIGN=MIDDLE  ALT=\"c=-48\"   DISABLED_style= \"max-width:90%; height:auto;\" >)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+=+%28-35+%2B-+sqrt%28+%2835%29%5E2-4%2A-1%2A-48+%29%29%2F%282%2A-1%29 ALIGN=MIDDLE  ALT=\"p+=+%28-35+%2B-+sqrt%28+%2835%29%5E2-4%2A-1%2A-48+%29%29%2F%282%2A-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in a=-1, b=35, and c=-48\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+=+%28-35+%2B-+sqrt%28+1225-4%2A-1%2A-48+%29%29%2F%282%2A-1%29 ALIGN=MIDDLE  ALT=\"p+=+%28-35+%2B-+sqrt%28+1225-4%2A-1%2A-48+%29%29%2F%282%2A-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square 35 to get 1225  \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+=+%28-35+%2B-+sqrt%28+1225%2B-192+%29%29%2F%282%2A-1%29 ALIGN=MIDDLE  ALT=\"p+=+%28-35+%2B-+sqrt%28+1225%2B-192+%29%29%2F%282%2A-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%2A-48%2A-1 ALIGN=MIDDLE  ALT=\"-4%2A-48%2A-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-192 ALIGN=MIDDLE  ALT=\"-192\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+=+%28-35+%2B-+sqrt%28+1033+%29%29%2F%282%2A-1%29 ALIGN=MIDDLE  ALT=\"p+=+%28-35+%2B-+sqrt%28+1033+%29%29%2F%282%2A-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms in the radicand (everything under the square root)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+=+%28-35+%2B-+sqrt%281033%29%29%2F%282%2A-1%29 ALIGN=MIDDLE  ALT=\"p+=+%28-35+%2B-+sqrt%281033%29%29%2F%282%2A-1%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" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+=+%28-35+%2B-+sqrt%281033%29%29%2F-2 ALIGN=MIDDLE  ALT=\"p+=+%28-35+%2B-+sqrt%281033%29%29%2F-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 2 and -1 to get -2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So now the expression breaks down into two parts\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+=+%28-35+%2B+sqrt%281033%29%29%2F-2 ALIGN=MIDDLE  ALT=\"p+=+%28-35+%2B+sqrt%281033%29%29%2F-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+=+%28-35+-+sqrt%281033%29%29%2F-2 ALIGN=MIDDLE  ALT=\"p+=+%28-35+-+sqrt%281033%29%29%2F-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Now break up the fraction\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=-35%2F-2%2Bsqrt%281033%29%2F-2 ALIGN=MIDDLE  ALT=\"p=-35%2F-2%2Bsqrt%281033%29%2F-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=-35%2F-2-sqrt%281033%29%2F-2 ALIGN=MIDDLE  ALT=\"p=-35%2F-2-sqrt%281033%29%2F-2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Simplify\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=35+%2F+2-sqrt%281033%29%2F2 ALIGN=MIDDLE  ALT=\"p=35+%2F+2-sqrt%281033%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=35+%2F+2%2Bsqrt%281033%29%2F2 ALIGN=MIDDLE  ALT=\"p=35+%2F+2%2Bsqrt%281033%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So these expressions approximate to\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=1.4298413200118 ALIGN=MIDDLE  ALT=\"p=1.4298413200118\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=33.5701586799882 ALIGN=MIDDLE  ALT=\"p=33.5701586799882\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "So our possible solutions are:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=1.4298413200118 ALIGN=MIDDLE  ALT=\"p=1.4298413200118\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=33.5701586799882 ALIGN=MIDDLE  ALT=\"p=33.5701586799882\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "However, when we plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=33.5701586799882 ALIGN=MIDDLE  ALT=\"p=33.5701586799882\"   DISABLED_style= \"max-width:90%; height:auto;\" > into either equation, we get a negative value. So the only solution is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=1.4298413200118 ALIGN=MIDDLE  ALT=\"p=1.4298413200118\"   DISABLED_style= \"max-width:90%; height:auto;\" > which rounds to $1.43 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );