Solve....x(x-3)=x-9

x^2 - 3x = x - 9

x^2 - 4x + 9 = 0

x = 2 +/- sqrt(5)i

To solve the equation x(x-3) = x-9, we need to simplify and rearrange the terms to isolate x. Here's how to do it step by step:

1. Distribute the x to both terms within the parentheses:
x^2 - 3x = x - 9

2. Move all terms to one side of the equation by subtracting x and adding 9 to both sides:
x^2 - 3x - x + 9 = 0

Simplifying this expression gives:
x^2 - 4x + 9 = 0

3. Now we have a quadratic equation in the standard form: ax^2 + bx + c = 0. Here, a = 1, b = -4, and c = 9.

4. To solve this quadratic equation, we can use the quadratic formula:
x = (-b ± √(b^2-4ac)) / (2a)

Plugging in the values, we have:
x = (4 ± √((-4)^2 - 4(1)(9))) / (2(1))

5. Simplifying further:
x = (4 ± √(16 - 36)) / 2

x = (4 ± √(-20)) / 2

Here, we have a negative number under the square root, indicating that the equation has no real solutions. The square root of a negative number is not defined within the realm of real numbers.

Therefore, the equation x(x-3) = x-9 has no real solutions.