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.
  
  ${x}^{3} = \frac{1}{4} \cdot x$
  
  => $4 {x}^{3} = x$
  
  => $4 {x}^{3} - x = 0$
  
  => $x \left(4 {x}^{2} - 1\right) = 0$
  
  => $x \left(4 {x}^{2} - 1\right) = 0$
  
  => $x \left({\left(2 x\right)}^{2} - {\left(1\right)}^{2}\right) = 0$
  
  => $x \left(2 x + 1\right) \left(2 x - 1\right) = 0$
  
  $x = 0 \mathmr{and} x = - \frac{1}{2} \mathmr{and} x = \frac{1}{2}$