Answer:
(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
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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