SOLUTION: The demand and supply equations for a certain item are given by D = –5p + 40 S = –p2 + 30p – 8 Find the equilibrium price.

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Question 121605: The demand and supply equations for a certain item are given by
D = –5p + 40
S = –p2 + 30p – 8
Find the equilibrium price.

Answer by checkley71(8403) About Me  (Show Source):
You can put this solution on YOUR website!
[y=-5x+40] (red line) & [y=-x^2+30x-8] (green line)
-5P+40=-P^2+30P-8
P^2-5P-30P+40+8=0
P^2-35P+48=0
USING THE QUADRATIC EQUATION WE GET:
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
P=(35+-SQRT[-35^2-4*1*48])/2*1
P=(35+-SQRT[1225-192])/2
P=(35+-SQRT1033])/2
P=(35+-32.14)/2
P=(35+32.14)/2
P=67.14/2
P=33.57 ANSWER.
P=(35-32.14)/2
P=2.86/2
P=1.43 ANSWER.
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A GRAPHIC SOLUTION IS:


+graph%28+500%2C500%2C+-60%2C+50%2C+-50%2C+240%2C+y+=+-5x+%2B40+%2C+y+=+-x%5E2+%2B30x+-8%29+ (graph 500x500 pixels, x from -60 to 50, y from -50 to 240, of TWO functions y = -5x +40 and y = -x^2 +30x -8).