4d) $x^2 + 5x = 14$
$= x^2 + 5x - 14 = 0$
$= (x - 2)(x + 7)$
$= x = 2 \text{ or } -7$

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Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Quadratic Equations", "Standard Form Conversion", "Factoring Trinomials", "Null Factor Law" ], "new_concepts": [], "current_concepts": [ "Quadratic Equations", "Standard Form Conversion", "Factoring Trinomials", "Null Factor Law" ] } ## Convert to standard form $$ \begin{aligned} x^2 + 5x &= 14 \ x^2 + 5x - 14 &= 0 \end{aligned} $$ ## Factor the quadratic trinomial $$ \begin{aligned} (x - 2)(x + 7) = 0 \end{aligned} $$ ## Solve for x $$ \begin{aligned} x - 2 = 0 &\implies x = 2 \ x + 7 = 0 &\implies x = -7 \ x &= 2 \text{ or } -7 \end{aligned} $$ $x = 2$ or $-7$ { "subject": "Mathematics", "question_type": "Free Response", "knowledge_point": [ "Mathematics", "Algebra", "Quadratic Equations" ] }

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Convert to standard form

Factor the quadratic trinomial

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