If the cost, c(x), for manufacturing x units of a certain product is given by c(x)=x^2-14x+74, find the number of units manufactured at a cost of $9050

So for this, since C(x) is the cost, and we are given the cost of $9050, we will plug 9050 into C(x) and solve for x:

So for this, I will be completing the square. Firstly, subtract 74 on both sides of the equation:

Next, we want to make the right side of the equation a perfect square. To find the constant of this soon-to-be perfect square, you need to divide the x coefficient by 2, square the quotient, then add the result on both sides of the equation. In this case:

-14 ÷ 2 = -7, (-7)² = 49

Next, factor the left side:

Next, square root both sides:

Next, add 7 to both sides:

Next, solve the left side twice. Once with the plus symbol, once with the minus symbol:

Since we cannot have negative units in this context, at the cost of $9050 you can manufacture 102 units.

.mp4 files, because, video

step-by-step explanation:

1. practice, practice & more practice

2. review errors

3. master the key concepts

do not try to memorise the processes.

4. understand your doubts.

5. create a distraction free study environment

6. create a mathematical dictionary

7. apply maths to real world problems.