question

solve for $x$ by factoring: $5x^2 + 36x + 7 = 0$.

write the two solutions in the answer template below.

provide your answer below:

$x = \square, \square$

Question

question

solve for $x$ by factoring: $5x^2 + 36x + 7 = 0$.

write the two solutions in the answer template below.

provide your answer below:

$x = \square, \square$

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": [ "AC Method", "Factoring by Grouping", "Zero Product Property", "Solving Linear Equations" ], "new_concepts": [], "current_concepts": [ "AC Method", "Factoring by Grouping", "Zero Product Property", "Solving Linear Equations" ] } ## Identify the coefficients Using the *AC Method* knowledge point $$ \begin{aligned} &a = 5,\quad b = 36,\quad c = 7\ &a \cdot c = 5 \cdot 7 = 35 \end{aligned} $$ ## Split the middle term Using the *AC Method* knowledge point $$ \begin{aligned} &35 \cdot 1 = 35\ &35 + 1 = 36\ &5x^2 + 35x + x + 7 = 0 \end{aligned} $$ ## Factor by grouping Using the *Factoring by Grouping* knowledge point $$ \begin{aligned} &5x(x + 7) + 1(x + 7) = 0\ &(5x + 1)(x + 7) = 0 \end{aligned} $$ ## Apply the zero product property Using the *Zero Product Property* knowledge point $$ \begin{aligned} &5x + 1 = 0 \quad \text{or} \quad x + 7 = 0 \end{aligned} $$ ## Solve for x Using the *Solving Linear Equations* knowledge point $$ \begin{aligned} &x = -\frac{1}{5},\quad x = -7 \end{aligned} $$ Solve for $x$ by factoring: $5x^2 + 36x + 7 = 0$. Write the two solutions in the answer template below. Provide your answer below: $x =$ $-\frac{1}{5}$, $-7$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Trinomial Factorization" ] }

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QUESTION IMAGE

Question

Explanation:

Identify the coefficients

Split the middle term

Factor by grouping

Apply the zero product property

Solve for x

Answer: