The given quadratic equation is expressed as
x^2 - 6x - 27 = 0
x^2 - 6x = 27
We would apply the method of completing the square. In this method, we would add square of halve the coefficient of x to both sides of the equation. The coefficient of x is - 6. Half of - 6 is - 3. Square of - 3 is (- 3)^2. Thus, we have
x^2 - 6x + (- 3)^2 = 27 + (- 3)^2
(x - 3)^2 = 27 + 9
(x - 3)^2 = 36
The third option is correct