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If you have a linear expression, ax + b, and you square it, then you get,

   a^2x^2 +2abx + b^2    --------- (1)

You have,

9x^2-18x+3 ------------------------- (2)

and you want this to be in the same format as (1).

Rearranging (2),

3^2x^2 - 2*3*3x + 3

You can see that the coefficient of x^2 is 9, which is 3^2, so a = 3.

Since a = 3, then 2a = 6 and this gives b = -3.

Now that we have b, we simply add and subtract b^2 to let us complete the square.

3^2x^2 - 2*3*3x + 3^3 - 3^2 + 3

(3x - 3)^2 - 9 + 3

(3x - 3)^2 - 6

by Level 11 User (81.5k points)

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