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

rick has $1400 and sally has $1500

step-by-step explanation:

to find amount of money rick has after 10 years :

principal = $1000 , time = 10 years , rate = 4% annually

to find amount of money sally has after 10 years :

her friend gives to pay her $50 per year, therefore money she has after 10 years = 50 × 10 = $500

also, sally gets $1000 after 10 years,

therefore, total amount of money sally has after 10 years = 500 + 1000 = $1500

so, after 10 years : rick has $1400 and sally has $1500