SOLUTION: Quadratic application If the cost ,C(x) for manufactoring x units of a certain product is given by C(x)=x^2-125x+50, find thye units manufactored at a cost of $9500

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Question 301003: Quadratic application
If the cost ,C(x) for manufactoring x units of a certain product is given by
C(x)=x^2-125x+50, find thye units manufactored at a cost of $9500
Answer by nerdybill(7384) (Show Source):
You can put this solution on YOUR website!
If the cost ,C(x) for manufactoring x units of a certain product is given by
C(x)=x^2-125x+50, find thye units manufactored at a cost of $9500
.
The given quadratic:
C(x)=x^2-125x+50
where
C(x) is the cost
x is the number of units
.
Simply plug in the given cost and solve for x:
C(x)=x^2-125x+50
9500 = x^2-125x+50
0 = x^2-125x-9450
Apply the quadratic formula when then yields:
x = {178.07, -53.07}
.
Throw out the negative solution leaving:
x = 178 units
.
Details of quadratic formula follows:

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=53425 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 178.069243313262, -53.0692433132622. Here's your graph: