Answer:
Widgets should be sold by $38.88 to maximize the profit.
Step-by-step explanation:
Vertex of a quadratic function:
Suppose we have a quadratic function in the following format:

It's vertex is the point 
In which


Where

If a<0, the vertex is a maximum point, that is, the maximum value happens at
, and it's value is
.
In this question:
The profit is given by:

Which is a quadratic function with 
The maximum profit happens at the x of the vertex. Thus

Widgets should be sold by $38.88 to maximize the profit.
Subtract 4 from both sides, solve using quadratic formula
ax^2+bx+c
(-b(+or-) Square Root of b^2 - 4ac)/2a
9x^2+9x-4=0
-9(+or-)Square root of 9^2-4(9)(-4)/2(9)
Solve^
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Answer: 6
Solution: 2(4-3) + 2(5-3) = 8-6+10-6=6