Solution for Problem 1.3.4

 Solve for x:  (3x – 1)2 = 9      Square Root Method

Solve

Step

3x – 1 = ± 3

Take square root of both sides

3x – 1 = -3 or 3x – 1 = 3

Solve each equation separately
3x – 1 = -3 Solve first equation
3x = -2

x = -2/3

3x – 1 = 3 Solve second equation
3x = 4

x = 4/3

Check 

If x  = -2/3, then
 (3(-2/3) – 1)2 = 9   
 (-2 – 1)2 = 9
 (-3)2 = 9   

If x  = 4/3, then
  (3(4/3) – 1)2 = 9   
  (4 – 1)2 = 9
  (3)2 = 9