solve the following equation by factoring. write your answer in reduced fraction form, if necessary.

\y^2 + 13y + 42 = 0\

Question

solve the following equation by factoring. write your answer in reduced fraction form, if necessary.

\y^2 + 13y + 42 = 0\

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": [ "Factoring Trinomials", "Zero Product Property", "Solving Quadratic Equations" ], "new_concepts": [], "current_concepts": [ "Solving Quadratic Equations", "Factoring Trinomials", "Zero Product Property" ] } ## Identify the quadratic equation We are given the quadratic equation to solve: $$ y^2 + 13y + 42 = 0 $$ ## Factor the quadratic trinomial Using the **Factoring Trinomials** knowledge point $$ \begin{aligned} &y^2 + 13y + 42 = (y + 6)(y + 7) \end{aligned} $$ ## Apply the zero product property Using the **Zero Product Property** knowledge point $$ \begin{aligned} &y + 6 = 0 \quad \text{or} \quad y + 7 = 0 \end{aligned} $$ ## Solve for the variable Using the **Solving Quadratic Equations** knowledge point $$ \begin{aligned} &y = -6 \quad \text{or} \quad y = -7 \end{aligned} $$ Solve the following equation by factoring. Write your answer in reduced fraction form, if necessary. $y^2 + 13y + 42 = 0$ $y =$ -6 , $y =$ -7 { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Solving Quadratic Equations" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the quadratic equation

Factor the quadratic trinomial

Apply the zero product property

Solve for the variable

Answer: