solve:
\(x-2)(x-7)=x-7\

Question

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Factoring Quadratics", "Zero Product Property", "Solving Quadratic Equations" ], "new_concepts": [], "current_concepts": [ "Factoring Quadratics", "Zero Product Property", "Solving Quadratic Equations" ] } ## Rearrange the equation to set it to zero $$ \begin{aligned} (x-2)(x-7) &= x-7 \ (x-2)(x-7) - (x-7) &= 0 \end{aligned} $$ ## Factor out the common binomial term $$ \begin{aligned} (x-7)[(x-2) - 1] &= 0 \ (x-7)(x-3) &= 0 \end{aligned} $$ ## Apply the zero product property to find the solutions $$ \begin{aligned} x - 7 = 0 &\implies x = 7 \ x - 3 = 0 &\implies x = 3 \end{aligned} $$ Solve: $$(x-2)(x-7) = x-7$$ $x =$ $3, 7$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Solving Quadratic Equations" ] }

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Question

Explanation:

Rearrange the equation to set it to zero

Factor out the common binomial term

Apply the zero product property to find the solutions

Answer: