(x-3)^2 >=(x+6)*(x-1)

To solve the inequality (x-3)^2 >= (x+6)(x-1), we must first expand both sides and then simplify the inequality to solve for x.

Let's start by expanding both sides:

On the left side, we expand (x-3)^2:

(x-3)^2 = x^2 - 6x + 9

On the right side, we expand (x+6)(x-1):

(x+6)(x-1) = x^2 - x + 6x - 6 = x^2 + 5x - 6

Now our inequality looks like this:

x^2 - 6x + 9 >= x^2 + 5x - 6

Next, let's subtract x^2 from both sides to cancel the quadratic term, as it appears on both sides of the inequality:

- 6x + 9 >= 5x - 6

Now, we will bring like terms to the same side by adding 6x to both sides and by adding 6 to both sides:

9 + 6 >= 5x + 6x

15 >= 11x

Next, divide both sides by 11 to solve for x:

x <= 15/11

So the solution to the inequality is x <= 15/11 or approximately x <= 1.3636.