Solve for x: (x + 1)^2 − 3(x − 1) = 4. Choose the correct value of x.

Introduction / Context:This is a straightforward quadratic simplification leading to a linear factorization. Expand the square, distribute the subtraction, and collect like terms to solve for x. The options include simple rational or integer candidates.

Given Data / Assumptions:

• Equation: (x + 1)^2 − 3(x − 1) = 4
• All real solutions are admissible.

Concept / Approach:Expand (x + 1)^2, distribute −3 across (x − 1), then move all terms to one side to get a factorable expression. Solve the resulting equation and pick the matching option.

Step-by-Step Solution:Expand: (x + 1)^2 = x^2 + 2x + 1Distribute: −3(x − 1) = −3x + 3Sum: x^2 + 2x + 1 − 3x + 3 = 4 ⇒ x^2 − x + 4 = 4Simplify: x^2 − x = 0 ⇒ x(x − 1) = 0Solutions: x = 0 or x = 1

Verification / Alternative check:Plug x = 0: LHS = 1 − (−3) = 4 = RHS. Plug x = 1: LHS = 4 − 0 = 4. Both work; among the listed options, 0 is explicitly present.

Why Other Options Are Wrong:−2, 1/2, −1 are not solutions of x(x − 1) = 0; 1 is also a valid solution but not marked correct here since the single correct choice is specified as 0.

Common Pitfalls:Algebraic slips when expanding or moving the 4; forgetting there can be two solutions before matching with discrete options.

Final Answer:0