Let's first simplify the left side of the equation:
(6-x)(x+6) - (x-11)x
= 6x + 36 - x^2 - 6x - x^2 + 11x= 6x + 36 - 2x^2 + 11x= 17x + 36 - 2x^2
Now, let's set this expression equal to 36:
17x + 36 - 2x^2 = 36
Now, we can simplify this equation further by moving all terms to one side:
17x + 36 - 2x^2 - 36 = 017x - 2x^2 = 0
Next, we can factor out an x from the equation:
x(17 - 2x) = 0
Now, we have two possibilities:
Therefore, the solutions to the equation are x = 0 and x = 8.5.
Let's first simplify the left side of the equation:
(6-x)(x+6) - (x-11)x
= 6x + 36 - x^2 - 6x - x^2 + 11x
= 6x + 36 - 2x^2 + 11x
= 17x + 36 - 2x^2
Now, let's set this expression equal to 36:
17x + 36 - 2x^2 = 36
Now, we can simplify this equation further by moving all terms to one side:
17x + 36 - 2x^2 - 36 = 0
17x - 2x^2 = 0
Next, we can factor out an x from the equation:
x(17 - 2x) = 0
Now, we have two possibilities:
x = 017 - 2x = 017 = 2x
x = 8.5
Therefore, the solutions to the equation are x = 0 and x = 8.5.