9x^2 -6x+6 in the form (ax+b)^2 +c

Question

a, b and c are constants 

Answer 1

9x² - 6x + 6

9x² - 6x + 1 + 5

(3x - 1)² + 5

Answer 2

9x² - 6x  + 6

Divide through by 9:

 

x² - (6/9)x + 6/9

x² - (2/3)x + 2/3

 

To complete the square take half of the coefficient

of the x term, square it, add and subtract that:

 

(1/2)(-2/3) = -1/3

(-1/3)² = 1/9

 

x² - (2/3)x + 1/9 - 1/9 + 2/3

(x - 1/3)² - 1/9 + 2/3

(x - 1/3)² + 5/9

 

Is this in form (ax + b)² + c ?

Yes it is: a=1, b=-1/3, c=5/9