How do I Rewrite the function by completing the square x^2+8x-29

  (x +4)^2 -45

Step-by-step explanation:

The square of a binomial has the form ...

  (x +a)^2 = x^2 +2ax +a^2

That is, the constant term (a^2) is the square of half the coefficient of the linear term: (2a/2)^2 = a^2.

To "complete the square", you add 0 in the form of the desired constant added to its opposite. Here, we want the constant for the square to be (8/2)^2 = 16. So, we can add 0 = 16 -16 to the expression:

  x^2 +8x +16 -29 -16

  (x^2 +8x +16) -45 . . . . group the terms that make the square

  (x +4)^2 -45 . . . . rewritten after completing the square