solve the following quadratic equation by factoring. separate multiple answers with a comma.

\2x^2 - 5x = 12\

Question

solve the following quadratic equation by factoring. separate multiple answers with a comma.

\2x^2 - 5x = 12\

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": [ "Standard Form of Quadratic Equations", "Factoring Quadratic Equations", "Zero Product Property", "Solving Quadratic Equations" ], "new_concepts": [], "current_concepts": [ "Standard Form of Quadratic Equations", "Factoring Quadratic Equations", "Zero Product Property", "Solving Quadratic Equations" ] } ## Write in standard form Using the *Standard Form of Quadratic Equations* knowledge point $$ \begin{aligned} 2x^2 - 5x &= 12 \ 2x^2 - 5x - 12 &= 0 \end{aligned} $$ ## Factor the quadratic expression Using the *Factoring Quadratic Equations* knowledge point $$ \begin{aligned} 2x^2 - 8x + 3x - 12 &= 0 \ 2x(x - 4) + 3(x - 4) &= 0 \ (2x + 3)(x - 4) &= 0 \end{aligned} $$ ## Apply zero product property Using the *Zero Product Property* knowledge point $$ \begin{aligned} 2x + 3 = 0 \quad &\text{or} \quad x - 4 = 0 \end{aligned} $$ ## Solve for x Using the *Solving Quadratic Equations* knowledge point $$ \begin{aligned} x = -\frac{3}{2} \quad &\text{or} \quad x = 4 \end{aligned} $$ Solve the following quadratic equation by factoring. Separate multiple answers with a comma. $2x^2 - 5x = 12$ $x =$ $-\frac{3}{2}, 4$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Solving Quadratic Equations" ] }

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QUESTION IMAGE

Question

Explanation:

Write in standard form

Factor the quadratic expression

Apply zero product property

Solve for x

Answer: