<h2>Steps:</h2>
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:
![9050=x^2-14x+74](https://tex.z-dn.net/?f=9050%3Dx%5E2-14x%2B74)
So for this, I will be completing the square. Firstly, subtract 74 on both sides of the equation:
![8976=x^2-14x](https://tex.z-dn.net/?f=8976%3Dx%5E2-14x)
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
![9025=x^2-14x+49](https://tex.z-dn.net/?f=9025%3Dx%5E2-14x%2B49)
Next, factor the left side:
![9025=(x-7)^2](https://tex.z-dn.net/?f=9025%3D%28x-7%29%5E2)
Next, square root both sides:
![\pm\ 95=x-7](https://tex.z-dn.net/?f=%5Cpm%5C%2095%3Dx-7)
Next, add 7 to both sides:
![7\pm 95=x](https://tex.z-dn.net/?f=7%5Cpm%2095%3Dx)
Next, solve the left side twice. Once with the plus symbol, once with the minus symbol:
![102,-88=x](https://tex.z-dn.net/?f=102%2C-88%3Dx)
<h2>Answer:</h2>
Since we cannot have negative units in this context, <u>at the cost of $9050 you can manufacture 102 units.</u>