Question

6 calcula las raíces de la ecuación cuadrática.

\\(\text{incógnita}^2 - 5x - 36 = 0\\)

\\(\text{incógnita} = \\) \\(y \text{incógnita} = \\)

Explanation:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"blank_filling_formatter",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [
"Trinomial Factoring"
],
"new_concepts": [
"Quadratic Equations",
"Solving Quadratics by Factoring"
],
"current_concepts": [
"Trinomial Factoring",
"Quadratic Equations",
"Solving Quadratics by Factoring"
]
}
</pre_analysis>

<reasoning>

Factorizar la ecuación cuadrática

\[

$$\begin{aligned} &x^2 - 5x - 36 = 0 \\ &(x - 9)(x + 4) = 0 \end{aligned}$$

\]

Resolver para la incógnita

\[

$$\begin{aligned} &x - 9 = 0 \implies x = 9 \\ &x + 4 = 0 \implies x = -4 \end{aligned}$$

\]
</reasoning>

<answer>
Calcula las raíces de la ecuación cuadrática.

\(x^2 - 5x - 36 = 0\)

incógnita = <blank>\(9\)</blank> y incógnita = <blank>\(-4\)</blank>
</answer>

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

Answer:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"blank_filling_formatter",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [
"Trinomial Factoring"
],
"new_concepts": [
"Quadratic Equations",
"Solving Quadratics by Factoring"
],
"current_concepts": [
"Trinomial Factoring",
"Quadratic Equations",
"Solving Quadratics by Factoring"
]
}
</pre_analysis>

<reasoning>

Factorizar la ecuación cuadrática

\[

$$\begin{aligned} &x^2 - 5x - 36 = 0 \\ &(x - 9)(x + 4) = 0 \end{aligned}$$

\]

Resolver para la incógnita

\[

$$\begin{aligned} &x - 9 = 0 \implies x = 9 \\ &x + 4 = 0 \implies x = -4 \end{aligned}$$

\]
</reasoning>

<answer>
Calcula las raíces de la ecuación cuadrática.

\(x^2 - 5x - 36 = 0\)

incógnita = <blank>\(9\)</blank> y incógnita = <blank>\(-4\)</blank>
</answer>

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