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) About Me  (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 ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B1x%2B-10+=+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=%281%29%5E2-4%2A1%2A-10=41.

Discriminant d=41 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-1%2B-sqrt%28+41+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%281%29%2Bsqrt%28+41+%29%29%2F2%5C1+=+2.70156211871642
x%5B2%5D+=+%28-%281%29-sqrt%28+41+%29%29%2F2%5C1+=+-3.70156211871642

Quadratic expression 1x%5E2%2B1x%2B-10 can be factored:
1x%5E2%2B1x%2B-10+=+1%28x-2.70156211871642%29%2A%28x--3.70156211871642%29
Again, the answer is: 2.70156211871642, -3.70156211871642. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B1%2Ax%2B-10+%29