the square of a number is 12 less than 7 times the number. what is the number?

-4 or -3
-4 or 3
-3 or 4
3 or 4

Question

the square of a number is 12 less than 7 times the number. what is the number?

-4 or -3
-4 or 3
-3 or 4
3 or 4

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Solving Quadratic Equations", "Quadratic Equation Formulation" ], "new_concepts": [], "current_concepts": [ "Solving Quadratic Equations", "Quadratic Equation Formulation" ] } ## Formulate the quadratic equation Let $x$ be the number. $$ x^2 = 7x - 12 $$ ## Rearrange into standard form $$ x^2 - 7x + 12 = 0 $$ ## Solve by factoring $$ \begin{aligned} &(x - 3)(x - 4) = 0 \ &x = 3 \quad \text{or} \quad x = 4 \end{aligned} $$

(A) $-4$ or $-3$

(B) $-4$ or $3$

(C) $-3$ or $4$

(D) $3$ or $4$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Solving Quadratic Equations" ] }

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QUESTION IMAGE

Question

Explanation:

Formulate the quadratic equation

Rearrange into standard form

Solve by factoring

Answer: