Question

current objective
solve a factored quadratic equation using the zero product

question

solve: \\((w)(3w + 5) = 0\\). multiple answers, if any, should be separated by a comma.

provide your answer below:

\\(w =\\)

Explanation:

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"concepts_used": [
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</pre_analysis>

<reasoning>

Apply the Zero Product Property

Using the Zero Product Property knowledge point
\[

$$\begin{aligned} &(w)(3w + 5) = 0 \\ &w = 0 \quad \text{or} \quad 3w + 5 = 0 \end{aligned}$$

\]

Solve the linear equations

Using the Solving Linear Equations knowledge point
\[

$$\begin{aligned} &w = 0 \\ &3w + 5 = 0 \implies 3w = -5 \implies w = -\frac{5}{3} \end{aligned}$$

\]
</reasoning>

<answer>
Solve: \((w)(3w + 5) = 0\). Multiple answers, if any, should be separated by a comma.

Provide your answer below:

\(w =\) <blank>\(0, -\frac{5}{3}\)</blank>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Algebra",
"Zero Product Property"
]
}
</post_analysis>

Answer:

<pre_analysis>
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"step_cot",
"blank_filling_formatter",
"explain_then_answer",
"tutor",
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],
"needs_drawing": false,
"concepts_used": [
"Zero Product Property",
"Solving Linear Equations"
],
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"current_concepts": [
"Zero Product Property",
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}
</pre_analysis>

<reasoning>

Apply the Zero Product Property

Using the Zero Product Property knowledge point
\[

$$\begin{aligned} &(w)(3w + 5) = 0 \\ &w = 0 \quad \text{or} \quad 3w + 5 = 0 \end{aligned}$$

\]

Solve the linear equations

Using the Solving Linear Equations knowledge point
\[

$$\begin{aligned} &w = 0 \\ &3w + 5 = 0 \implies 3w = -5 \implies w = -\frac{5}{3} \end{aligned}$$

\]
</reasoning>

<answer>
Solve: \((w)(3w + 5) = 0\). Multiple answers, if any, should be separated by a comma.

Provide your answer below:

\(w =\) <blank>\(0, -\frac{5}{3}\)</blank>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Algebra",
"Zero Product Property"
]
}
</post_analysis>