P=-5x^2+1000x+5000 how many computers must be sold to obtain a profit of $55,000.00?

14 computers

Step-by-step explanation:

Set the profit, p, equal to $55,000.00 and then solve for x:

-5x^2 + 1000x + 5000 = 55000

Dividing both sides by - 5 results in:

x^2 - 200x - 1000 = + 11000.

Combining the constant terms results in:

x^2 - 200x - 11000 = 0

Solve this by completing the square:

x^2 - 200x + 10000 - 10000 - 11000 = 0, or

(x - 100) ^2 - 21000 = 0, or

(x - 100) ^2 = 21000

Taking the square root of both sides, we get

x - 100 = ±10√210, or

x = 100 ± 10√210, or approx. x = 100 + 14.5, or approx 114.5

Sellilng between 114 and 115 computers would result in a profit of $55,000.