text: # If x^3 = 1/4x, what is the possible value of x?
  
  Jun 27, 2016
  
  $x = 0 \mathmr{and} x = - \frac{1}{2} \mathmr{and} x = \frac{1}{2}$
  
  #### Explanation:
  
  Factorize the above equation to get the possible values of x.
  
  ${x}^{3} = \frac{1}{4} \cdot x$
  
  => $4 {x}^{3} = x$
  
  => $4 {x}^{3} - x = 0$
  
  => $x \left(4 {x}^{2} - 1\right) = 0$
  
  => $x \left(4 {x}^{2} - 1\right) = 0$
  
  => $x \left({\left(2 x\right)}^{2} - {\left(1\right)}^{2}\right) = 0$
  
  => $x \left(2 x + 1\right) \left(2 x - 1\right) = 0$
  
  $x = 0 \mathmr{and} x = - \frac{1}{2} \mathmr{and} x = \frac{1}{2}$
explanation: The document contains a math question and its corresponding answer. The question asks for the possible values of \( x \) given the equation \( x^3 = \frac{1}{4}x \), and the answer provides the solutions \( x = 0 \), \( x = -\frac{1}{2} \), and \( x = \frac{1}{2} \).
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: # If x^3 = 1/4x, what is the possible value of x?
  
  Jun 27, 2016
  
  $x = 0 \mathmr{and} x = - \frac{1}{2} \mathmr{and} x = \frac{1}{2}$
  
  #### Explanation:
  
  Factorize the above equation to get the possible values of x.
  
  ${x}^{3} = \frac{1}{4} \cdot x$
  
  => $4 {x}^{3} = x$
  
  => $4 {x}^{3} - x = 0$
  
  => $x \left(4 {x}^{2} - 1\right) = 0$
  
  => $x \left(4 {x}^{2} - 1\right) = 0$
  
  => $x \left({\left(2 x\right)}^{2} - {\left(1\right)}^{2}\right) = 0$
  
  => $x \left(2 x + 1\right) \left(2 x - 1\right) = 0$
  
  $x = 0 \mathmr{and} x = - \frac{1}{2} \mathmr{and} x = \frac{1}{2}$
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document contains a math question and its corresponding answer. The question asks for the possible values of \( x \) given the equation \( x^3 = \frac{1}{4}x \), and the answer provides the solutions \( x = 0 \), \( x = -\frac{1}{2} \), and \( x = \frac{1}{2} \).
  
  Label: question-and-answer