If the cost see for manufacturing X units of a certain product is given by C=X squared +25X +40 find the number of units manufactured at a cost of 9390

Answer:   85 unitsStep-by-step explanation:Fill in the given value and solve for x.   c = x² +25x +40   9390 = x² +25x + 40   x² +25x -9350 = 0 . . . . . . rearrange to standard form   (x +110)(x -85) = 0 . . . . . . . factor the quadraticThe positive solution is the value of x that makes a factor be zero: x = 85.The number of units manufactured at a cost of 9390 is 85 units._____There are several ways you can solve the quadratic. There appear to be no restrictions here, so we used a graphing calculator to assist. It shows the zeros of the equation to be -110 and +85, so the factors are as shown above.__The prime factorization of 9350 is ...   9350 = 2 · 5² · 11 · 17so there are 24 divisors:   1, 2, 5, 10, 11, 17, 22, 25, 34, 50, 55, 85, 110, 170, 187, 275, 374, 425, 550, 850, 935, 1870, 4675, 9350We're looking for two factors that differ by a relatively small amount, so we would start with the factors near the middle of this list:   9350 = 85·110 . . . . . these differ by 25, so are the factors of interestThese let you rewrite the 25x term so you can factor by grouping:   x² +110x -85x +9350 = 0 . . . . rewrite the middle term   x(x +110) -85(x +110) = 0 . . . . . factor each pair of terms   (x -85)(x +110) = 0 . . . . . . . . . . factor out the common factorThe solution of interest is x = 85.__You can also "complete the square"   x² +25x = 9350   x² +25x + 156.25 = 9506.25   (x² +12.5) = 97.5² . . . . . rewrite as squares   x = 97.5 -12.5 = 85 . . . . take the positive square root