SOLUTION: This ? is hard please help? The demand and supply equations for a certain item are given by D=-5p+40 S=-p^2+30p-8 find the equilibrium price. a. $1.57 b. $1.71 c. $1.4

Question 102585: This ? is hard please help?
The demand and supply equations for a certain item are given by
D=-5p+40
S=-p^2+30p-8
find the equilibrium price.
a. $1.57
b. $1.71
c. $1.43
d.$1.29
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
To find the equilibrium price, set the two equations equal to one another

Add 5p and subtract 40 from both sides to get everything to one side

Combine like terms

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 possible solutions are:
or

However, when we plug in into either equation, we get a negative value. So the only solution is which rounds to $1.43. So the answer is C
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