To solve the equation, we need to first simplify it:
(x-2)(x-1)x - x^2 - x/2 = 4.5(x^2 - 3x + 2)*x - x^2 - x/2 = 4.5x^3 - 3x^2 + 2x - x^2 - x/2 = 4.5x^3 - 4x^2 + 2x - x/2 = 4.5x
Now, let's combine like terms:
x^3 - 4x^2 + 2x - x/2 - 4.5x = x^3 - 4x^2 - 1.5x = 0
Now, let's solve for x. There are a few ways to do this; one way is by factoring out an x:
x(x^2 - 4x - 1.5) = 0
Now, we can set each factor equal to zero:
x = 0
To find the other solutions, we can use the quadratic formula:
x = [4 ± sqrt(16 + 6)] / x = [4 ± sqrt(22)] / x = (4 ± √22) / 2
Therefore, the solutions to the equation are:
x = 0, (4 + √22) / 2, (4 - √22) / 2
To solve the equation, we need to first simplify it:
(x-2)(x-1)x - x^2 - x/2 = 4.5
(x^2 - 3x + 2)*x - x^2 - x/2 = 4.5
x^3 - 3x^2 + 2x - x^2 - x/2 = 4.5
x^3 - 4x^2 + 2x - x/2 = 4.5x
Now, let's combine like terms:
x^3 - 4x^2 + 2x - x/2 - 4.5x =
x^3 - 4x^2 - 1.5x = 0
Now, let's solve for x. There are a few ways to do this; one way is by factoring out an x:
x(x^2 - 4x - 1.5) = 0
Now, we can set each factor equal to zero:
x = 0
To find the other solutions, we can use the quadratic formula:
x = [4 ± sqrt(16 + 6)] /
x = [4 ± sqrt(22)] /
x = (4 ± √22) / 2
Therefore, the solutions to the equation are:
x = 0, (4 + √22) / 2, (4 - √22) / 2