SOLUTION: The demand and supply equations for a certain item are given by D = 5p + 40 S= -p^2 + 30p -8 Find the equilibrium Price. I am needing serious help with this. I am lost with

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Question 76107: The demand and supply equations for a certain item are given by
D = 5p + 40
S= -p^2 + 30p -8
Find the equilibrium Price.
I am needing serious help with this. I am lost with this problem and need some help. Thanks.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
The demand and supply equations for a certain item are given by
D = 5p + 40
S= -p^2 + 30p -8
Find the equilibrium Price.
:
Equilibrium occurs when Demand = Supply, (D=S)
:
5p + 40 = -p^2 + 30p - 8
:
Form a quadratic equation on the left
+p^2 + 5p - 30p + 40 + 8 = 0
:
p^2 - 25p + 48 = 0
:
Use the quadratic equation to find p: a=1; b=-25; c=48:
p+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
:
p+=+%28-%28-25%29+%2B-+sqrt%28+-25%5E2+-+4+%2A+1+%2A+48+%29%29%2F%282%2A1%29+
:
p+=+%28%2B25+%2B-+sqrt%28+625+-+192+%29%29%2F%282%29+
:
p+=+%28%2B25+%2B-+sqrt%28+433+%29%29%2F%282%29+
:
p+=+%28%2B25+%2B+20.8%29%2F%282%29+
:
p+=+%28%2B45.8%29%2F%282%29+
p = 22.9
and
p+=+%28%2B25+-+20.8%29%2F%282%29+
:
p+=+%28%2B4.2%29%2F%282%29+
p = 2.1
:
Check solution using p = 2.1, are both equations equal?
5p + 40 =
5(2.1) + 40 = 50.5
and
-p^2 + 30p = 8 +
-(2.1^2) +30(2.1) -8 =
- 4.41 + 63 - 8 = 50.6; a slight difference because our solution is not exact