Question

question

solve: (99a^2 + 55a = 0). multiple answers, if any, should be separated by

provide your answer below:

(a = )

Explanation:

<pre_analysis>
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"blank_filling_formatter",
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"concepts_used": [
"Greatest Common Factor Factoring",
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<reasoning>

Factor out the greatest common factor

Using the Greatest Common Factor Factoring knowledge point
\[

$$\begin{aligned} &99a^2 + 55a = 0 \\ &11a(9a + 5) = 0 \end{aligned}$$

\]

Apply the zero product property

Using the Zero Product Property knowledge point
\[

$$\begin{aligned} &11a = 0 \quad \text{or} \quad 9a + 5 = 0 \end{aligned}$$

\]

Solve each linear equation

Using the Solving Linear Equations knowledge point
\[

$$\begin{aligned} &a = 0 \\ &9a = -5 \implies a = -\frac{5}{9} \end{aligned}$$

\]
</reasoning>

<answer>
Solve: \(99a^2 + 55a = 0\). Multiple answers, if any, should be separated by commas.

Provide your answer below:

\(a =\) <blank>\(0, -\frac{5}{9}\)</blank>
</answer>

<post_analysis>
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"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Algebra",
"Greatest Common Factor Factoring"
]
}
</post_analysis>

Answer:

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

<reasoning>

Factor out the greatest common factor

Using the Greatest Common Factor Factoring knowledge point
\[

$$\begin{aligned} &99a^2 + 55a = 0 \\ &11a(9a + 5) = 0 \end{aligned}$$

\]

Apply the zero product property

Using the Zero Product Property knowledge point
\[

$$\begin{aligned} &11a = 0 \quad \text{or} \quad 9a + 5 = 0 \end{aligned}$$

\]

Solve each linear equation

Using the Solving Linear Equations knowledge point
\[

$$\begin{aligned} &a = 0 \\ &9a = -5 \implies a = -\frac{5}{9} \end{aligned}$$

\]
</reasoning>

<answer>
Solve: \(99a^2 + 55a = 0\). Multiple answers, if any, should be separated by commas.

Provide your answer below:

\(a =\) <blank>\(0, -\frac{5}{9}\)</blank>
</answer>

<post_analysis>
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"subject": "Mathematics",
"question_type": "Fill-in-the-blank",
"knowledge_point": [
"Mathematics",
"Algebra",
"Greatest Common Factor Factoring"
]
}
</post_analysis>