document.write( "Question 122059: D=-200p + 35,000The supply equation is predicted to be
\n" ); document.write( "S= -p^2 +400p –20,000Find the equilibrium price. \n" ); document.write( "
Algebra.Com's Answer #89668 by ankor@dixie-net.com(22740)\"\" \"About 
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D =-200p + 35,000 The supply equation is predicted to be
\n" ); document.write( "S = -p^2 +400p –20,000 Find the equilibrium price.
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\n" ); document.write( "I assume you mean that equilibrium price (p) occurs when D = S, so we have;
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\n" ); document.write( "-200p + 35000 = -p^2 + 400p - 20000
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\n" ); document.write( "Arrange as a quadratic equation on the left:
\n" ); document.write( "+p^2 - 200p - 400p + 35000 + 20000 = 0
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\n" ); document.write( "p^2 - 600p + 55000 = 0
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\n" ); document.write( "Use the quadratic formula to find p:
\n" ); document.write( "a = 1; b = -600; c = 55000
\n" ); document.write( "\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"
\n" ); document.write( ":
\n" ); document.write( "\"p+=+%28-%28-600%29+%2B-+sqrt%28-600%5E2+-+4+%2A+1+%2A+55000+%29%29%2F%282%2A1%29+\"
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\n" ); document.write( "\"p+=+%28600+%2B-+sqrt%28360000+-+220000+%29%29%2F%282%29+\"
\n" ); document.write( ":
\n" ); document.write( "\"p+=+%28600+%2B-+sqrt%28140000%29%29%2F%282%29+\"
\n" ); document.write( ":
\n" ); document.write( "\"p+=+%28600+%2B-+374.166%29%2F%282%29+\"; found the square root of 140000
\n" ); document.write( "Solution 1
\n" ); document.write( "\"p+=+%28600+%2B+374.166%29%2F%282%29+\";
\n" ); document.write( "\"p+=+%28974.166%29%2F%282%29+\";
\n" ); document.write( "p = $487.08
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\n" ); document.write( "Solution 2:
\n" ); document.write( "\"p+=+%28600+-+374.166%29%2F%282%29+\";
\n" ); document.write( "\"p+=+%28225.834%29%2F%282%29+\";
\n" ); document.write( "p = $112.92
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\n" ); document.write( "You should check both solutions by substitution in the original equation\r
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