the product of some negative number and 2 less than twice that number is 760. find the number.

the negative number is (type an integer or a simplified fraction.)

Question

the product of some negative number and 2 less than twice that number is 760. find the number.

the negative number is   (type an integer or a simplified fraction.)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Quadratic Equations", "Quadratic Formula Application" ], "new_concepts": [], "current_concepts": [ "Quadratic Equations", "Quadratic Formula Application", "Algebraic Expressions" ] } ## Set up the quadratic equation $$ \begin{aligned} &\text{Let } x \text{ be the negative number, where } x < 0.\ &x(2x - 2) = 760\ &2x^2 - 2x - 760 = 0\ &x^2 - x - 380 = 0 \end{aligned} $$ ## Solve the quadratic equation $$ \begin{aligned} &(x - 20)(x + 19) = 0\ &x = 20 \quad \text{or} \quad x = -19 \end{aligned} $$ ## Select the negative solution $$ \begin{aligned} &x < 0 \implies x = -19 \end{aligned} $$ The negative number is -19 (Type an integer or a simplified fraction.) { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Quadratic Equations" ] }

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Explanation:

Set up the quadratic equation

Solve the quadratic equation

Select the negative solution

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