document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=98233>Question 98233</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The demand and supply equations for a certain item are given by:<BR>\n" );
document.write( "D=-5p+10<BR>\n" );
document.write( "S=-p^2+30p-8<BR>\n" );
document.write( "Find both possible solutions and determine the equilibrium price\r<BR>\n" );
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document.write( "This is what I have so far:<BR>\n" );
document.write( "-5p+40=-p^2+30p-8<BR>\n" );
document.write( "p^2-35p+48=0<BR>\n" );
document.write( "p^2-36p=-48   I am now unsure of what to do from here.\r<BR>\n" );
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document.write( "Thank you for your help </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #71391 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=71391\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To find the equilibrium, set the equations equal to one another\r<BR>\n" );
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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" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%5E2-35p%2B48=0 ALIGN=MIDDLE  ALT=\"p%5E2-35p%2B48=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Get all terms to one side and combine like terms\r<BR>\n" );
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document.write( "Let's use the quadratic formula to solve for p:\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=ap%5E2%2Bbp%2Bc=0 ALIGN=MIDDLE  ALT=\"ap%5E2%2Bbp%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=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" );
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document.write( "So lets solve <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p%5E2-35%2Ap%2B48=0 ALIGN=MIDDLE  ALT=\"p%5E2-35%2Ap%2B48=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" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+=+%28--35+%2B-+sqrt%28+%28-35%29%5E2-4%2A1%2A48+%29%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"p+=+%28--35+%2B-+sqrt%28+%28-35%29%5E2-4%2A1%2A48+%29%29%2F%282%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in a=1, b=-35, and c=48\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+=+%2835+%2B-+sqrt%28+%28-35%29%5E2-4%2A1%2A48+%29%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"p+=+%2835+%2B-+sqrt%28+%28-35%29%5E2-4%2A1%2A48+%29%29%2F%282%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Negate -35 to get 35\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+=+%2835+%2B-+sqrt%28+1225-4%2A1%2A48+%29%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"p+=+%2835+%2B-+sqrt%28+1225-4%2A1%2A48+%29%29%2F%282%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square -35 to get 1225  (note: remember when you square -35, you must square the negative as well. This is because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-35%29%5E2=-35%2A-35=1225 ALIGN=MIDDLE  ALT=\"%28-35%29%5E2=-35%2A-35=1225\"   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=p+=+%2835+%2B-+sqrt%28+1225%2B-192+%29%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"p+=+%2835+%2B-+sqrt%28+1225%2B-192+%29%29%2F%282%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%2A48%2A1 ALIGN=MIDDLE  ALT=\"-4%2A48%2A1\"   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" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+=+%2835+%2B-+sqrt%28+1033+%29%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"p+=+%2835+%2B-+sqrt%28+1033+%29%29%2F%282%2A1%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=p+=+%2835+%2B-+sqrt%281033%29%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"p+=+%2835+%2B-+sqrt%281033%29%29%2F%282%2A1%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=p+=+%2835+%2B-+sqrt%281033%29%29%2F2 ALIGN=MIDDLE  ALT=\"p+=+%2835+%2B-+sqrt%281033%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 2 and 1 to get 2\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=p+=+%2835+%2B+sqrt%281033%29%29%2F2 ALIGN=MIDDLE  ALT=\"p+=+%2835+%2B+sqrt%281033%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+=+%2835+-+sqrt%281033%29%29%2F2 ALIGN=MIDDLE  ALT=\"p+=+%2835+-+sqrt%281033%29%29%2F2\"   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=p=%2B35%2F2%2Bsqrt%281033%29%2F2 ALIGN=MIDDLE  ALT=\"p=%2B35%2F2%2Bsqrt%281033%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=%2B35%2F2-sqrt%281033%29%2F2 ALIGN=MIDDLE  ALT=\"p=%2B35%2F2-sqrt%281033%29%2F2\"   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=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;\" > or <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;\" >\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=p=33.5701586799882 ALIGN=MIDDLE  ALT=\"p=33.5701586799882\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <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;\" >\r<BR>\n" );
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document.write( "So our possible solutions are:\r<BR>\n" );
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document.write( "<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;\" > or <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;\" >\r<BR>\n" );
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document.write( "However, since <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;\" > generates a negative supply and demand, 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;\" > </SPAN>\n" );
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