Rewrite the function by completing the square.
f(x)=x^2+8x−29
f(x)=(x+__)^2+__

The resulting function by completing the square is f(x) = (x+ 4)²  - 45

Given the function

f(x) = x² + 8x - 29

The function can also be grouped like this:

f(x) = (x² + 8x) - 29

Completing the square of the function in parenthesis

f(x) = (x² + 8x) - 29

To do that, we will add the square of the half of the coefficient of x:

Coefficient of x = 8

half of Coefficient of x = 8/2 = 4

Squaring the result = 4² = 16

The function will then become:

f(x) = (x² + 8x + 16 - 16) - 29

f(x) = (x² + 8x + 16) - 16 - 29

f(x) = (x² + 8x + 16) - 45

Factorizing the function in bracket:

f(x) = (x+ 4)²  - 45

Hence the resulting function by completing the square is f(x) = (x+ 4)²  - 45

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(x + 4)² - 45

Step-by-step explanation:

Given

x² + 8x - 29

To complete the square

add/ subtract ( half the coefficient of the x- term)² to x² + 8x

f(x) = x² + 2(4)x + 16 - 16 - 29

     = (x + 4)² - 45