Find the zeros of f (x) = x^2 + 7x + 9

-7/2 ±1/2sqrt (13) = x

Step-by-step explanation:

f (x) = x^2 + 7x + 9

To find the zeros, set this equal to zero

0 = x^2 + 7x + 9

I will complete the square

Subtract 9 from each side

0-9 = x^2 + 7x + 9-9

-9 = x^2 + 7x

Take the coefficient of the x term, 7

divide by 2, 7/2

Then square it, (7/2) ^2 = 49/4

Add this to both sides

-9 + 49/4=x^2 + 7x + 49/4

-36/4 + 49/4 = (x+7/2) ^2

13/4 = (x+7/2) ^2

Take the square root of each side

±sqrt (13/4) = sqrt ((x+7/2) ^2)

± sqrt (13) / sqrt (4) = (x+7/2)

± 1/2 sqrt (13) = (x+7/2)

Subtract 7/2 from each side

-7/2 ±1/2sqrt (13) = x+7/2-7/2

-7/2 ±1/2sqrt (13) = x