SOLUTION: The demand and supply equations for a certain item are given by D = �5p + 40 S = �p2 + 30p � 8Find the equilibrium price. A) $1.57 B) $1.29 C) $1.71 D) $1.43

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Question 90634: The demand and supply equations for a certain item are given by D = �5p + 40 S = �p2 + 30p � 8Find the equilibrium price.
A) $1.57 B) $1.29 C) $1.71 D) $1.43

Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
Set D equal to S

get everything to one side

Let's use the quadratic formula to solve for p:

Starting with the general quadratic

the general solution using the quadratic equation is:

So lets solve ( notice , , and )

Plug in a=-1, b=35, and c=-48

Square 35 to get 1225

Multiply to get

Combine like terms in the radicand (everything under the square root)

Simplify the square root (note: If you need help with simplifying the square root, check out this solver)

Multiply 2 and -1 to get -2

So now the expression breaks down into two parts

or

Now break up the fraction

or

Simplify

or

So these expressions approximate to

or

So our solutions are:
or

Since 1.4298413200118 rounds to 1.43, the answer is D)