solve
\5x^2 + 18x = 8\

Question

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 Quadratics", "Zero Product Property" ], "new_concepts": [], "current_concepts": [ "Factoring Quadratics", "Zero Product Property", "Solving Quadratic Equations" ] } ## Write the equation in standard form Using the *Factoring Quadratics* knowledge point $$ \begin{aligned} 5x^2 + 18x &= 8 \ 5x^2 + 18x - 8 &= 0 \end{aligned} $$ ## Factor the quadratic expression Using the *Factoring Quadratics* knowledge point $$ \begin{aligned} &5x^2 + 20x - 2x - 8 = 0 \ &5x(x + 4) - 2(x + 4) = 0 \ &(5x - 2)(x + 4) = 0 \end{aligned} $$ ## Solve for x Using the *Zero Product Property* knowledge point $$ \begin{aligned} 5x - 2 = 0 &\implies x = \frac{2}{5} \ x + 4 = 0 &\implies x = -4 \end{aligned} $$ Solve $5x^2 + 18x = 8$ $x = \frac{2}{5}, -4$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Solving Quadratic Equations" ] }

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Question

Explanation:

Write the equation in standard form

Factor the quadratic expression

Solve for x

Answer: