SOLUTION: Could someone please help me solve this word problem? The demand equation for a certain type of printer is given by {{{D=-200p+35000}}} The supply equation is predicted to be

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Question 101578: Could someone please help me solve this word problem?
The demand equation for a certain type of printer is given by
D=-200p%2B35000
The supply equation is predicted to be S=-p%5E2%2B400p-20000
Find the equilibrium price.
Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
I am guessing that when supply=demand then there is equilibrium and the demand equation equals the supply equation.
-200p+35000=-p^2+400p-20000
p^2-600p+55000=0
p=113, p=487
Ed
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-600x%2B55000+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-600%29%5E2-4%2A1%2A55000=140000.

Discriminant d=140000 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--600%2B-sqrt%28+140000+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-600%29%2Bsqrt%28+140000+%29%29%2F2%5C1+=+487.082869338697
x%5B2%5D+=+%28-%28-600%29-sqrt%28+140000+%29%29%2F2%5C1+=+112.917130661303

Quadratic expression 1x%5E2%2B-600x%2B55000 can be factored:
1x%5E2%2B-600x%2B55000+=+%28x-487.082869338697%29%2A%28x-112.917130661303%29
Again, the answer is: 487.082869338697, 112.917130661303. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-600%2Ax%2B55000+%29

graph%28500%2C500%2C-500%2C750%2C-50000%2C50000%2Cx%5E2-600x%2B55000%29