Question

solving quadratic equations
example 2
solve: \\(x^2 = 144\\)
solution
value: 3
match the items.
a. \\(\pm 12\\)
b. 144
c. positive

1. \\(c = ?\\)
2. \\(\sqrt{144}\\)
3. \\(c\\) is a ______ integer.

since \\(c > 0\\), the given quadratic equation has two solutions.
\\(x^2 = 144\\)
\\(x = \pm 12\\)
thus, \\(x = 12\\) or \\(x = -12\\).
example 3
solve: \\(x^2 = -3\\)

Explanation:

<pre_analysis>
{
"quality": "clear",
"question_count": 3,
"skills_matched": [
"step_cot",
"table_formatter",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [
"Quadratic Equations"
],
"new_concepts": [],
"current_concepts": [
"Quadratic Equations"
]
}
</pre_analysis>

<reasoning>

Identify the value of c

\[
c = 144
\]

Evaluate the square root of c

\[
\sqrt{144} = 12
\]

Determine the classification of c

\[
c = 144 \implies \text{positive}
\]
</reasoning>

<answer>

No.	Problem	Answer
2	\(\sqrt{144}\)	a. \(\pm 12\)
3	\(c\) is a \(\underline{\qquad}\) integer.	c. positive

</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multi-part",
"knowledge_point": [
"Mathematics",
"Algebra",
"Quadratic Equations"
]
}
</post_analysis>

Answer:

<pre_analysis>
{
"quality": "clear",
"question_count": 3,
"skills_matched": [
"step_cot",
"table_formatter",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [
"Quadratic Equations"
],
"new_concepts": [],
"current_concepts": [
"Quadratic Equations"
]
}
</pre_analysis>

<reasoning>

Identify the value of c

\[
c = 144
\]

Evaluate the square root of c

\[
\sqrt{144} = 12
\]

Determine the classification of c

\[
c = 144 \implies \text{positive}
\]
</reasoning>

<answer>

No.	Problem	Answer
2	\(\sqrt{144}\)	a. \(\pm 12\)
3	\(c\) is a \(\underline{\qquad}\) integer.	c. positive

</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multi-part",
"knowledge_point": [
"Mathematics",
"Algebra",
"Quadratic Equations"
]
}
</post_analysis>