SOLUTION: The weekly profit of a company depends on the number of employees working during the week. It is represented by the formula P = x2 + x � 10 where x is the average number of employe

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Question 210679: The weekly profit of a company depends on the number of employees working during the week. It is represented by the formula P = x2 + x � 10 where x is the average number of employees working on each day of the week. For what values of �x� is the profit positive?

Answer by nerdybill(7384) (Show Source):
You can put this solution on YOUR website!
They give you:
P = x^2 + x � 10
.
Set P to zero to find out when you have NO profit:
0 = x^2 + x � 10
.
Solving for x will give you where it crosses the x-axis:
0 = x^2 + x � 10
Since we can't factor, we apply the quadratic equation to get:
x = {2.7, -3.7}
We can throw out the negative solution leaving:
x = 2.7
.
Values of x where P is POSITIVE:
x > 2.7
.
Details of quadratic to follow:

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=41 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 2.70156211871642, -3.70156211871642. Here's your graph: