solve the equation $6t^2 = 7t - 2$

answer: $t =$

give your answers as integers or reduced fractions, separated by commas.

Question

solve the equation $6t^2 = 7t - 2$

answer: $t =$

give your answers as integers or reduced fractions, separated by commas.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Factoring Quadratics", "Zero Product Property" ], "new_concepts": [], "current_concepts": [ "Factoring Quadratics", "Zero Product Property", "Quadratic Equations" ] } ## Rearrange the quadratic equation into standard form Subtract $7t$ and add $2$ to both sides of the equation to set it to zero: $$ 6t^2 - 7t + 2 = 0 $$ ## Factor the quadratic expression Using the **Factoring Quadratics** knowledge point $$ \begin{aligned} &6t^2 - 7t + 2 = 0\ &6t^2 - 3t - 4t + 2 = 0\ &3t(2t - 1) - 2(2t - 1) = 0\ &(3t - 2)(2t - 1) = 0 \end{aligned} $$ ## Solve for t Using the **Zero Product Property** knowledge point $$ \begin{aligned} &3t - 2 = 0 \implies t = \frac{2}{3}\ &2t - 1 = 0 \implies t = \frac{1}{2} \end{aligned} $$ Solve the equation $6t^2 = 7t - 2$ Answer: $t =$ $\frac{2}{3}, \frac{1}{2}$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Quadratic Equations" ] }

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Question

Explanation:

Rearrange the quadratic equation into standard form

Factor the quadratic expression

Solve for t

Answer: