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

\5x^2 - 7x = 6\

$x =$

Question

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

\5x^2 - 7x = 6\

$x =$

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" ], "new_concepts": [], "current_concepts": [ "Standard Form of Quadratic Equations", "Factoring Quadratic Equations", "Zero Product Property", "Solving Quadratic Equations" ] } ## Write the equation in standard form Using the *Standard Form of Quadratic Equations* knowledge point $$ 5x^2 - 7x - 6 = 0 $$ ## Factor the quadratic expression Using the *Factoring Quadratic Equations* knowledge point $$ \begin{aligned} &5x^2 - 10x + 3x - 6 = 0\ &5x(x - 2) + 3(x - 2) = 0\ &(5x + 3)(x - 2) = 0 \end{aligned} $$ ## Apply the zero product property to solve Using the *Zero Product Property* knowledge point $$ \begin{aligned} &5x + 3 = 0 \implies x = -\frac{3}{5}\ &x - 2 = 0 \implies x = 2 \end{aligned} $$ Solve the following quadratic equation by factoring. Separate multiple answers with a comma. $5x^2 - 7x = 6$ $x =$ $-\frac{3}{5}, 2$ { "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 equation in standard form

Factor the quadratic expression

Apply the zero product property to solve

Answer: