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solve: \\(22p^2 = 352\\) -16, 16 -4, 4

Question

solve: \\(22p^2 = 352\\)

-16, 16
-4, 4

Explanation:

Response

<pre_analysis>
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<reasoning>

Isolate the squared term

\[

$$\begin{aligned} 22p^2 &= 352 \\ p^2 &= \frac{352}{22} \\ p^2 &= 16 \end{aligned}$$

\]

Solve for p

\[

$$\begin{aligned} p &= \pm\sqrt{16} \\ p &= \pm 4 \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>(A) -16, 16</mcq-option>
<mcq-correct>(B) -4, 4</mcq-correct>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Algebra",
"Quadratic Equations"
]
}
</post_analysis>

Answer:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"multiple_choice_formatter",
"explain_then_answer",
"quick"
],
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"concepts_used": [
"Quadratic Equations"
],
"new_concepts": [],
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"Quadratic Equations"
]
}
</pre_analysis>

<reasoning>

Isolate the squared term

\[

$$\begin{aligned} 22p^2 &= 352 \\ p^2 &= \frac{352}{22} \\ p^2 &= 16 \end{aligned}$$

\]

Solve for p

\[

$$\begin{aligned} p &= \pm\sqrt{16} \\ p &= \pm 4 \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>(A) -16, 16</mcq-option>
<mcq-correct>(B) -4, 4</mcq-correct>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Algebra",
"Quadratic Equations"
]
}
</post_analysis>