document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=93477>Question 93477</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 4. The demand equation for a certain computer chip is given by D=-15p+145 The supply equation is predicted to be S=-p^2+45p-270 Find the equilibrium price. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #68058 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=68058\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "To find the equilibrium price, set the two 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=-15p%2B145=-p%5E2%2B45p-270 ALIGN=MIDDLE  ALT=\"-15p%2B145=-p%5E2%2B45p-270\"   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=145=-p%5E2%2B45p-270%2B15p ALIGN=MIDDLE  ALT=\"145=-p%5E2%2B45p-270%2B15p\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add 15p to both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=-p%5E2%2B45p-270%2B15p-145 ALIGN=MIDDLE  ALT=\"0=-p%5E2%2B45p-270%2B15p-145\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 145 to both sides\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=-p%5E2%2B60p-415 ALIGN=MIDDLE  ALT=\"0=-p%5E2%2B60p-415\"   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 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%2B60%2Ap-415=0 ALIGN=MIDDLE  ALT=\"-p%5E2%2B60%2Ap-415=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=60 ALIGN=MIDDLE  ALT=\"b=60\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=-415 ALIGN=MIDDLE  ALT=\"c=-415\"   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+=+%28-60+%2B-+sqrt%28+%2860%29%5E2-4%2A-1%2A-415+%29%29%2F%282%2A-1%29 ALIGN=MIDDLE  ALT=\"p+=+%28-60+%2B-+sqrt%28+%2860%29%5E2-4%2A-1%2A-415+%29%29%2F%282%2A-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in a=-1, b=60, and c=-415\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+=+%28-60+%2B-+sqrt%28+3600-4%2A-1%2A-415+%29%29%2F%282%2A-1%29 ALIGN=MIDDLE  ALT=\"p+=+%28-60+%2B-+sqrt%28+3600-4%2A-1%2A-415+%29%29%2F%282%2A-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square 60 to get 3600  \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+=+%28-60+%2B-+sqrt%28+3600%2B-1660+%29%29%2F%282%2A-1%29 ALIGN=MIDDLE  ALT=\"p+=+%28-60+%2B-+sqrt%28+3600%2B-1660+%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-415%2A-1 ALIGN=MIDDLE  ALT=\"-4%2A-415%2A-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1660 ALIGN=MIDDLE  ALT=\"-1660\"   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+=+%28-60+%2B-+sqrt%28+1940+%29%29%2F%282%2A-1%29 ALIGN=MIDDLE  ALT=\"p+=+%28-60+%2B-+sqrt%28+1940+%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" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+=+%28-60+%2B-+2%2Asqrt%28485%29%29%2F%282%2A-1%29 ALIGN=MIDDLE  ALT=\"p+=+%28-60+%2B-+2%2Asqrt%28485%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" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p+=+%28-60+%2B-+2%2Asqrt%28485%29%29%2F-2 ALIGN=MIDDLE  ALT=\"p+=+%28-60+%2B-+2%2Asqrt%28485%29%29%2F-2\"   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+=+%28-60+%2B+2%2Asqrt%28485%29%29%2F-2 ALIGN=MIDDLE  ALT=\"p+=+%28-60+%2B+2%2Asqrt%28485%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+=+%28-60+-+2%2Asqrt%28485%29%29%2F-2 ALIGN=MIDDLE  ALT=\"p+=+%28-60+-+2%2Asqrt%28485%29%29%2F-2\"   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=-60%2F-2%2B2%2Asqrt%28485%29%2F-2 ALIGN=MIDDLE  ALT=\"p=-60%2F-2%2B2%2Asqrt%28485%29%2F-2\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=-60%2F-2-2%2Asqrt%28485%29%2F-2 ALIGN=MIDDLE  ALT=\"p=-60%2F-2-2%2Asqrt%28485%29%2F-2\"   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=30+-sqrt%28485%29 ALIGN=MIDDLE  ALT=\"p=30+-sqrt%28485%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=30%2Bsqrt%28485%29 ALIGN=MIDDLE  ALT=\"p=30%2Bsqrt%28485%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=p=7.97728445445476 ALIGN=MIDDLE  ALT=\"p=7.97728445445476\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=52.0227155455452 ALIGN=MIDDLE  ALT=\"p=52.0227155455452\"   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=7.97728445445476 ALIGN=MIDDLE  ALT=\"p=7.97728445445476\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=p=52.0227155455452 ALIGN=MIDDLE  ALT=\"p=52.0227155455452\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now lets check our possible answers:\r<BR>\n" );
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document.write( "Let's check the demand equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D=-15%287.98%29%2B145=25.3 ALIGN=MIDDLE  ALT=\"D=-15%287.98%29%2B145=25.3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in p=7.98 and simplify\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D=-15%2852.02%29%2B145=-635.3 ALIGN=MIDDLE  ALT=\"D=-15%2852.02%29%2B145=-635.3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in p=52.02 and simplify\r<BR>\n" );
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document.write( "Since the solution p=52.02 results in a negative demand, we need to discard this possible solution.\r<BR>\n" );
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document.write( "Let's check the supply equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S=-%287.98%29%5E2%2B45%287.98%29-270=25.4196 ALIGN=MIDDLE  ALT=\"S=-%287.98%29%5E2%2B45%287.98%29-270=25.4196\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in p=7.98 and simplify\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S=-%2852.02%29%5E2%2B45%2852.02%29-270=-635.1804 ALIGN=MIDDLE  ALT=\"S=-%2852.02%29%5E2%2B45%2852.02%29-270=-635.1804\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in p=52.02 and simplify\r<BR>\n" );
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document.write( "Since the solution p=52.02 results in a negative supply, we need to discard this possible solution.\r<BR>\n" );
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document.write( "So our only solution is p=7.98 </SPAN>\n" );
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