MODERATE EXERCISES - Symbol Manipulation

(6) Solve the following equations.

 (a) kx(k - x) = 0
   
 (b) 3x(3x + sqrt(2)) = 0
          
 (c) cx = cx(x + 0.5)

 (d) (2/3)(7x - )(x + 0.21) = 0
		

 (a) kx(k - x) = 0
     kx = 0, (k - x) = 0
      x = 0, or  k = x
    

 (b) 3x(3x + sqrt(2)) = 0
     3x = 0,    (3x + sqrt(2)) = 0
     x = 0,      3x = -(sqrt(2))
     x = 0, or   x = -(sqrt(2))/3                    

 (c) cx = cx(x + 0.5)
     cx - cx(x + 0.5) = 0
     cx[1 - (x + 0.5)] = 0
     cx = 0,   [1 - (x + 0.5)] = 0
      x = 0,   1 = x + 0.5
      x = 0,   (1 - 0.5) = x
      x = 0, or  x = 0.5

 (d) (2/3)(7x - )(x + 0.21) = 0
     (2/3)(7x - ) = 0, (x + 0.21) = 0
     (7x - ) = 0,     (x + 2.1) = 0
      7x = ,          x = -2.1
       x = /7,  or    x = -2.1