SOLUTION: The demand and supply equations for a certain item are given by {{{D=-5p+40}}} {{{S=-p^2+30p-8}}} Now find the equilibrium price. Could someone please help me i am lost?

Question 102615: The demand and supply equations for a certain item are given by Now find the equilibrium price.
Could someone please help me i am lost?

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
RELATED QUESTIONS
The demand and supply equations for a certain item are given by D=-5p+40 S=-p^2+30p-8 (answered by stanbon)

The demand and supply equations for a certain item are given by D = -5p + 40 S =... (answered by Nate)

The demand and supply equations for a certain item are given by: D=-5p+40 S=-p^2+30p-8 (answered by Nate)

Please help! The demand and supply equations for a certain item are given by: D= -5p... (answered by stanbon,scott8148)

The demand and supply equations for a certain item are given by D=-5p+40 S=-p^2+30p-8... (answered by rapaljer)

The demand and supply equations for a certain item are given by D=-5p+40 S=-p^2+30p-8 (answered by stanbon)

The demand and supply equations for a certain item are given by D = �5p + 40 S =... (answered by stanbon)

The demand and supply equations for a certain item are given by D = �5p + 40 S... (answered by elima)

The demand and supply equations for a certain item are given by D = �5p + 40 S... (answered by ankor@dixie-net.com)

The demand and supply equations for a certain item are given by D = �5p + 40 S... (answered by checkley71)