Question

question 16 points 3

solve: \\(x^2 + 21 = 142\\)

\\(x = -11\\) or \\(x = 11\\)

\\(x = -11\\) or \\(x = 1/11\\)

Explanation:

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

<reasoning>

Isolate the quadratic term

\[

$$\begin{aligned} x^2 + 21 &= 142 \\ x^2 &= 142 - 21 \\ x^2 &= 121 \end{aligned}$$

\]

Solve for x using square roots

\[

$$\begin{aligned} x &= \pm \sqrt{121} \\ x &= \pm 11 \\ x = -11 &\text{ or } x = 11 \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-correct>(A) \(x = -11\) or \(x = 11\)</mcq-correct>
<mcq-option>(B) \(x = -11\) or \(x = 1/11\)</mcq-option>
</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"
],
"needs_drawing": false,
"concepts_used": [
"Quadratic Equations"
],
"new_concepts": [],
"current_concepts": [
"Quadratic Equations"
]
}
</pre_analysis>

<reasoning>

Isolate the quadratic term

\[

$$\begin{aligned} x^2 + 21 &= 142 \\ x^2 &= 142 - 21 \\ x^2 &= 121 \end{aligned}$$

\]

Solve for x using square roots

\[

$$\begin{aligned} x &= \pm \sqrt{121} \\ x &= \pm 11 \\ x = -11 &\text{ or } x = 11 \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-correct>(A) \(x = -11\) or \(x = 11\)</mcq-correct>
<mcq-option>(B) \(x = -11\) or \(x = 1/11\)</mcq-option>
</answer>

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