document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=187638>Question 187638</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0132424355/algebrahomeworkh>mathematial analysis</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> If p represents price per unit in dollars and q represents the number of units per unit of time, find the equilibrium point.\r<BR>\n" );
document.write( "\n" );
document.write( "Supply: p= (q+10)^2 , Demand: p=388-16q-q^2\r<BR>\n" );
document.write( "\n" );
document.write( "With details<BR>\n" );
document.write( "Thank you, </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #140668 by </B><A HREF=/tutors/aboutme.mpl?userid=nerdybill><B>nerdybill(7384)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nerdybill><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/cgi-bin/show-face.mpl?user=nerdybill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=140668\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The equilibrium point is when supply and demand are equal.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Supply: p= (q+10)^2 , Demand: p=388-16q-q^2<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Notice BOTH equation defines 'p'.  Set them equal to each other then solve for 'q':<BR>\n" );
document.write( "(q+10)^2 = 388-16q-q^2<BR>\n" );
document.write( "Expanding the left side with FOIL:<BR>\n" );
document.write( "(q+10)^2 = 388-16q-q^2<BR>\n" );
document.write( "(q+10)(q+10) = 388-16q-q^2<BR>\n" );
document.write( "q^2 + 20q + 100 = 388-16q-q^2<BR>\n" );
document.write( "Move all terms to the left:<BR>\n" );
document.write( "2q^2 + 20q + 100 = 388-16q<BR>\n" );
document.write( "2q^2 + 36q + 100 = 388<BR>\n" );
document.write( "2q^2 + 36q - 288 = 0<BR>\n" );
document.write( "Divide both sides by 2:<BR>\n" );
document.write( "q^2 + 18q - 144 = 0<BR>\n" );
document.write( "Factoring the left:<BR>\n" );
document.write( "(q+24)(q-6) = 0<BR>\n" );
document.write( ".<BR>\n" );
document.write( "q = {-24, 6}<BR>\n" );
document.write( "A negative solution does not make sense so:<BR>\n" );
document.write( "q = 6\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );