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.

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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