The function f is defined by f (x) x2 - 6x + 21. What are the solutions of f (x) 0?

f (x) = x^2 - 6x + 21

0 = x^2-6x+21

subtract 21 from each side to prepare for completing the square

-21 = x^2 - 6x

completing the square (b/2) ^2

(-6/2) ^ = 3^2 = 9

add 9 to each side

-21 + 9 = x^2 - 6x + 9

-21 + 9 = (x-3) ^2

-12 = (x-3) ^2

take the square root of each side

+ - sqrt (-12) = x-3

add 3 to each side, take out the negative inside the square root

3 + - i sqrt (12) = x

simplify the square root sqrt (12) = sqrt (4) sqrt (3) = 2sqrt (3)

3 + - i 2sqrt (3) = x

Answer: 3+2isqrt (3)

3-2isqrt (3)