question

solve: $5m^2 - m - 6 = 0$. multiple answers, if any, s

provide your answer below:

$m = $

Question

question

solve: $5m^2 - m - 6 = 0$. multiple answers, if any, s

provide your answer below:

$m = $

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": [ "AC Method", "Factoring by Grouping", "Zero Product Property", "Solving Linear Equations" ], "new_concepts": [], "current_concepts": [ "AC Method", "Factoring by Grouping", "Zero Product Property", "Solving Linear Equations" ] } ## Identify the quadratic equation We need to solve the quadratic equation: $$5m^2 - m - 6 = 0$$ ## Factor the quadratic expression Using the *AC Method* and *Factoring by Grouping* knowledge points $$ \begin{aligned} &a \cdot c = 5 \cdot (-6) = -30\ &-6 + 5 = -1\ &5m^2 - 6m + 5m - 6 = 0\ &m(5m - 6) + 1(5m - 6) = 0\ &(5m - 6)(m + 1) = 0 \end{aligned} $$ ## Solve for the variable Using the *Zero Product Property* and *Solving Linear Equations* knowledge points $$ \begin{aligned} &5m - 6 = 0 \implies m = \frac{6}{5}\ &m + 1 = 0 \implies m = -1 \end{aligned} $$ Solve: $5m^2 - m - 6 = 0$. Multiple answers, if any, should be separated by a comma. Provide your answer below: $m =$ $\frac{6}{5}, -1$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Solving Quadratic Equations by Factoring" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the quadratic equation

Factor the quadratic expression

Solve for the variable

Answer: