Question

resuelve la ecuación usando raíces cuadradas. escribe tu trabajo en la página donde muestras tu trabajo.

seleccione todas las respuestas que correspondan.

\\((x - 7)^2 = 25\\)

a \\(-12\\)

b \\(10\\)

do \\(-2\\)

d \\(12\\)

mi ninguna solución

f \\(2\\)

Explanation:

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"Real Roots"
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"new_concepts": [
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<reasoning>

Aplicar la raíz cuadrada a ambos lados

\[

$$\begin{aligned} (x - 7)^2 &= 25 \\ x - 7 &= \pm\sqrt{25} \\ x - 7 &= \pm 5 \end{aligned}$$

\]

Resolver para x

\[

$$\begin{aligned} x &= 7 \pm 5 \\ x_1 &= 7 + 5 = 12 \\ x_2 &= 7 - 5 = 2 \end{aligned}$$

\]

Identificar las opciones correctas

\[

$$\begin{aligned} x &= 12 \quad \text{(Opción D)} \\ x &= 2 \quad \text{(Opción F)} \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>A - 12</mcq-option>
<mcq-option>B 10</mcq-option>
<mcq-option>do - 2</mcq-option>
<mcq-correct>D 12</mcq-correct>
<mcq-option>mi ninguna solución</mcq-option>
<mcq-correct>F 2</mcq-correct>
</answer>

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"question_type": "Multiple Choice",
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"Mathematics",
"Algebra",
"Quadratic Equations"
]
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</post_analysis>

Answer:

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"step_cot",
"multiple_choice_formatter",
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"Square Root Method"
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}
</pre_analysis>

<reasoning>

Aplicar la raíz cuadrada a ambos lados

\[

$$\begin{aligned} (x - 7)^2 &= 25 \\ x - 7 &= \pm\sqrt{25} \\ x - 7 &= \pm 5 \end{aligned}$$

\]

Resolver para x

\[

$$\begin{aligned} x &= 7 \pm 5 \\ x_1 &= 7 + 5 = 12 \\ x_2 &= 7 - 5 = 2 \end{aligned}$$

\]

Identificar las opciones correctas

\[

$$\begin{aligned} x &= 12 \quad \text{(Opción D)} \\ x &= 2 \quad \text{(Opción F)} \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>A - 12</mcq-option>
<mcq-option>B 10</mcq-option>
<mcq-option>do - 2</mcq-option>
<mcq-correct>D 12</mcq-correct>
<mcq-option>mi ninguna solución</mcq-option>
<mcq-correct>F 2</mcq-correct>
</answer>

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"question_type": "Multiple Choice",
"knowledge_point": [
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"Algebra",
"Quadratic Equations"
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