Answer:
40+ 10√10 and 40-10√10
Step-by-step explanation:
The two equations are 40x+300 and 80-0.5x^2
Substitute the given functions:
P(x)=(80x−0.5x^2)−(40x+300)P(x)=(80x−0.5x^2)−(40x+300)
P(x)=80x−0.5x^2−40x−300P(x)=80x−0.5x^2−40x−300
P(x)=−0.5x^2+40x−300P(x)=−0.5x^2+40x−300
Now, set up the equation for profit:
−0.5x^2+40x−300=50−0.5x^2+40x−300=50
To simplify, multiply the entire equation by -2 to eliminate the decimal:
x^2−80x+600=0
Now plug this into the quadratic formula
You should recieve 40±10√10