INTRODUCTORY EXERCISES - Symbol Manipulation

(7) Solve the following equations.

  
 (a) x(x + 3) = 0 

 (b) 2y = (1/2)y2 

 (c) (x - 2)(3x + 5) = 0

 (d) 3x(2x + 1)(x - 8) = 0

 (e) (x2 - 9x)(x + 4) = 0 
  

 (a) x(x + 3) = 0 
     x = 0 ,  (x + 3) = 0
               x = -3
     Thus, x = 0 or x = -3

 (b) 2y = (1/2)y2
     2y - (1/2)y2 = 0
      y(2 - (1/2)y) = 0
      y = 0,  2 - (1/2)y = 0
              2 = (1/2)y
              4 = y  
     Thus, y = 0 or y = 4 

 (c) (x - 2)(3x + 5) = 0
     (x - 2) = 0, (3x + 5) = 0
     x = 2 , 3x = -5
               x = (-5/3)
     Thus, x = 2 or x = (-5/3)

 (d) 3x(2x + 1)(x - 8) = 0
     3x = 0, (2x + 1) = 0, (x - 8) = 0
      x = 0,  2x = -1,    x = 8
              x = (-1/2)
     Thus, x = 0, x = (-1/2), or x = 8

 (e) (x2 - 9x)(x + 4) = 0
     (x2 - 9x) = 0, (x + 4) = 0
     x(x - 9) =0, x = -4
     Thus, x = 0, x = 9, x = -4