solve the equation: $3m^2 + m + 12 = 8$. full simplify your answer, including any non-real solutions.

$m =$

Question

solve the equation: $3m^2 + m + 12 = 8$. full simplify your answer, including any non-real solutions.

$m =$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Solving Quadratic Equations", "Quadratic Formula", "Complex Numbers" ], "new_concepts": [], "current_concepts": [ "Solving Quadratic Equations", "Quadratic Formula", "Complex Numbers" ] } ## Write the quadratic equation in standard form $$ \begin{aligned} 3m^2 + m + 12 &= 8 \ 3m^2 + m + 4 &= 0 \end{aligned} $$ ## Apply the quadratic formula $$ \begin{aligned} a = 3, \quad b &= 1, \quad c = 4 \ m &= \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \ m &= \frac{-1 \pm \sqrt{1^2 - 4(3)(4)}}{2(3)} \ m &= \frac{-1 \pm \sqrt{1 - 48}}{6} \ m &= \frac{-1 \pm \sqrt{-47}}{6} \end{aligned} $$ ## Simplify using the imaginary unit $$ m = \frac{-1 \pm i\sqrt{47}}{6} $$ Solve the equation: $3m^2 + m + 12 = 8$. Full simplify your answer, including any non-real solutions. $m =$ $\frac{-1 \pm i\sqrt{47}}{6}$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Solving Quadratic Equations" ] }

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QUESTION IMAGE

Question

Explanation:

Write the quadratic equation in standard form

Apply the quadratic formula

Simplify using the imaginary unit

Answer: