Question 537590: Your company has determined that the profit equation (in thousands of dollars) of producing x thousand smartphones is as follows:
Profit = –x2 + 110x – 1,000
(If the number of smartphones is 40,000, for example, then x = 40). The break-even point is the number of smartphones sold and produced that would result in a profit of zero.
Use your preferred method for solving the quadratic equation to determine the break-even point. Clearly demonstrate how the answer is determined, and interpret the result in real-life terms.
Answer by josmiceli(19441)   (Show Source):
You can put this solution on YOUR website! The equation is plotted x-y axes, except
Profit takes the place of y
A profit of zero will occur at the x-intercepts,
or the roots of the equation.
I can complete the square. first
Multiply both sides by 
Take 1/2 of the coefficient of x, square
it, then add it to both sides
Both sides are now "perfect squares"
Take the square root of both sides
And, taking the negative square root of  ,
There are two beak even points. One is at sales of
10,000 smartphones, and the other is at sales
of 100,000 smartphones
check:
(100,0)
OK
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