SOLUTION: Could someone please help me with this tricky word problem??? The demand and supply equations for a certain item are given by {{{D=-5p+40}}} {{{S=-p^2+30p-8}}} Find the equilib

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To find the equilibrium price, set the two equations equal to one another




Add 5p to both sides


Subtract 40 from 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=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, plugging in results in a negative demand. So the only solution is . So the equilibrium price is about $1.43