X2 - 12x -6=0
Complete the square

(x - 6)^2 = 42

Step-by-step explanation:

Using " ^ " to indicate exponentiation, we have:

x^2 - 12x -6=0

Here the coefficients of this quadratic equation are a = 1, b = -12 and c = -6.

Start by taking HALF of the coefficient of x, that is, HALF of -12.  We get -6.

Next, square this result:  (-6)^2 = 36.

Finally, add this 36 to both sides, obtaining:

x^2 - 12x + 36 - 6 = 36

Rewriting the first three terms, we get:

(x - 6)^2 - 6 = 36, or

(x - 6)^2 = 42   This is the end result to "completing the square."

If you want to go further and actually solve for x, then see below:

Taking the square root of both sides, we get

x - 6 = ±√42

Then x = 6 ± √42, or

x = 6 + √42 and

x = 6 - √42

so, converting firstly the mixed fractions to improper fractions and then "adding".