The cost to produce a product is modeled by the function f(x) = 5x2 − 70x + 258 where x is the number of products produced. Complete the square to determine the minimum cost of producing this product.

5(x − 7)2 + 13; The minimum cost to produce the product is $13.

5(x − 7)2 + 13; The minimum cost to produce the product is $7.

5(x − 7)2 + 258; The minimum cost to produce the product is $7.

5(x − 7)2 + 258; The minimum cost to produce the product is $258.

Question

The cost to produce a product is modeled by the function f(x) = 5x2 − 70x + 258 where x is the number of products produced. Complete the square to determine the minimum cost of producing this product.

 5(x − 7)2 + 13; The minimum cost to produce the product is $13.

 5(x − 7)2 + 13; The minimum cost to produce the product is $7.

 5(x − 7)2 + 258; The minimum cost to produce the product is $7.

 5(x − 7)2 + 258; The minimum cost to produce the product is $258.

blurbendy · Answer

Okay, it would be good to rewrite this in the form:
 x^2 -14x + 258 / 5 = 0
 Do you see how I got to this step?

blurbendy · Answer

yes, no, need me to explain?  this is only the first step.

anonymous · Answer

Yes i think i got it. Is it 5(x-7)^2 +13? @blurbendy?

blurbendy · Answer

Yes, but what is the minimum cost?

anonymous · Answer

Is it 13? @blurbendy

blurbendy · Answer

Nope, it's 7.

you have to solve for x, and you'll get 
x = 1/5(35 - i sqrt(65) )
and
x = 1/5 (35 + i sqrt(65) )

which is equal to 7 -1.6 and 7 + 1.6, which is basically just 7

anonymous · Answer

alright thanks :)

blurbendy · Answer

anytime!