solve the following equation by factoring. separate multiple answers with a comma.
\-9 = (x + 1)(x + 7)\

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Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "FOIL Method", "Polynomial Addition", "Factoring Trinomials", "Zero Product Property", "Solving Quadratic Equations" ], "new_concepts": [], "current_concepts": [ "FOIL Method", "Polynomial Addition", "Factoring Trinomials", "Zero Product Property", "Solving Quadratic Equations" ] } ## Expand the right side of the equation Using the *FOIL Method* knowledge point $$ \begin{aligned} (x+1)(x+7) &= x^2 + 7x + x + 7 \ &= x^2 + 8x + 7 \end{aligned} $$ ## Set the quadratic equation to zero Using the *Polynomial Addition* knowledge point $$ \begin{aligned} -9 &= x^2 + 8x + 7 \ 0 &= x^2 + 8x + 7 + 9 \ 0 &= x^2 + 8x + 16 \end{aligned} $$ ## Factor the quadratic trinomial Using the *Factoring Trinomials* knowledge point $$ \begin{aligned} x^2 + 8x + 16 &= (x+4)(x+4) \ &= (x+4)^2 \end{aligned} $$ ## Solve for x Using the *Zero Product Property* and *Solving Quadratic Equations* knowledge points $$ \begin{aligned} (x+4)^2 &= 0 \ x + 4 &= 0 \ x &= -4 \end{aligned} $$ $x = -4$ { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Solving Quadratic Equations" ] }

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Question

Explanation:

Expand the right side of the equation

Set the quadratic equation to zero

Factor the quadratic trinomial

Solve for x

Answer: