SOLUTION: 4. The demand equation for a certain computer chip is given by D=-15p+145 The supply equation is predicted to be S=-p^2+45p-270 Find the equilibrium price.

Question 93477: 4. The demand equation for a certain computer chip is given by D=-15p+145 The supply equation is predicted to be S=-p^2+45p-270 Find the equilibrium price.
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 15p to both sides

Subtract 145 to both sides

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=60, and c=-415

Square 60 to get 3600

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

Now lets check our possible answers:

Let's check the demand equation

Plug in p=7.98 and simplify

Plug in p=52.02 and simplify

Since the solution p=52.02 results in a negative demand, we need to discard this possible solution.

Let's check the supply equation

Plug in p=7.98 and simplify

Plug in p=52.02 and simplify

Since the solution p=52.02 results in a negative supply, we need to discard this possible solution.

So our only solution is p=7.98
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