Question 187638
The equilibrium point is when supply and demand are equal.
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Supply: p= (q+10)^2 , Demand: p=388-16q-q^2
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Notice BOTH equation defines 'p'.  Set them equal to each other then solve for 'q':
(q+10)^2 = 388-16q-q^2
Expanding the left side with FOIL:
(q+10)^2 = 388-16q-q^2
(q+10)(q+10) = 388-16q-q^2
q^2 + 20q + 100 = 388-16q-q^2
Move all terms to the left:
2q^2 + 20q + 100 = 388-16q
2q^2 + 36q + 100 = 388
2q^2 + 36q - 288 = 0
Divide both sides by 2:
q^2 + 18q - 144 = 0
Factoring the left:
(q+24)(q-6) = 0
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q = {-24, 6}
A negative solution does not make sense so:
q = 6