# 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.

Algebra ->  Algebra  -> Quadratic Equations and Parabolas -> 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.      Log On

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 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(28593)   (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