Factorise x2−30x+225 completely.

Sure, here are the steps to factorise the given expression:

1. The given expression is x^2 - 30x + 225.

2. We need to factorise this quadratic expression. A quadratic expression is factorised as (x-a)(x-b), where a and b are the roots of the equation.

3. The roots of the equation can be found using the formula x = [ -(-b) ± sqrt( (-b)^2 - 4ac ) ] / 2a. Here, a = 1 (coefficient of x^2), b = -30 (coefficient of x), and c = 225 (constant term).

4. However, in this case, we can see that the constant term 225 is a perfect square, and it's the square of 15. Also, the coefficient of x is -2*15 = -30. This suggests that the roots of the equation are 15 and 15.

5. Therefore, the factorised form of the given expression is (x-15)(x-15) or (x-15)^2.