the solutions to the equation (2x^2 + x - 1 = 2) are (x = \frac{-3}{2}) or (x = )

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{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Solving Quadratic Equations" ], "new_concepts": [], "current_concepts": [ "Solving Quadratic Equations" ] } ## Rearrange the quadratic equation into standard form $$ \begin{aligned} 2x^2 + x - 1 &= 2 \ 2x^2 + x - 3 &= 0 \end{aligned} $$ ## Factor the quadratic equation $$ \begin{aligned} (2x + 3)(x - 1) &= 0 \end{aligned} $$ ## Solve for the roots $$ \begin{aligned} 2x + 3 = 0 &\implies x = -\frac{3}{2} \ x - 1 = 0 &\implies x = 1 \end{aligned} $$ The solutions to the equation $2x^2 + x - 1 = 2$ are $x = \frac{-3}{2}$ or $x =$ 1 { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Solving Quadratic Equations" ] }

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Explanation:

Rearrange the quadratic equation into standard form

Factor the quadratic equation

Solve for the roots

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