Step-by-step explanation:
Certainly! Let’s solve the given equation step by step:
Distribute the terms inside the parentheses: [ x + 2(x - 1) + (x - 2)(x - 1) = 2 ]
Simplify each term: [ x + 2x - 2 + (x^2 - 3x + 2) = 2 ]
Combine like terms: [ x + 2x - 2 + x^2 - 3x + 2 = 2 ]
Rearrange the equation: [ x^2 - 2x + 2 = 2 ]
Subtract 2 from both sides: [ x^2 - 2x = 0 ]
Factor the left side: [ x(x - 2) = 0 ]
Now, we have two possible cases:
a) (x = 0) b) (x - 2 = 0)
For case (b), solve for (x): [ x - 2 = 0 ] [ x = 2 ]
Therefore, the solutions are (x = 0) and (x = 2)