SOLUTION: I need help with this problem 32. 3x2-x-2=0 solve for x by completing the square 3x2-x=2 x2-x/3+2/9= 2/3+2/9 (x-2/3)2= 6/9 x-2/3+6/9 x = 2/3 This is were I ge

I  need help with this problem

 32. 3x² - x - 2 = 0  solve for x by completing the square

solve for x by completing the square
     3x²-x=2  x²-x/3+2/9= 2/3+2/9 (x-2/3)2= 6/9 
     x-2/3+6/9  x = 2/3 This is were I get confused.

That's wrong! The 2/9 in the second step should be 1/36.

The rule is:

1. Multiply the coefficient of x by 1/2.  

-x/3 means (-1/3)x, so the coefficient of x is -1/3

We multiply that 1/2

(-1/3)(1/2) = -1/6

2. Square the result.

So we square -1/6 and get +1/36

3. Add that to both sides

      x2 - x/3 + 1/36 = 2/3 + 1/36  
               
           (x - 1/6)² = 24/36 + 1/36

           (x - 1/6)² = 25/36

Take square roots of both sides
                        
            x - 1/6 = ±5/6
                              
                  x = 1/6 ± 5/6 
                             
Using the + sign:

                  x = 1/6 + 5/6
                                 
                  x = 6/6
 
                  x = 1 

Using the - sign:

                  x = 1/6 - 5/6
                                 
                  x = -4/6
 
                  x = -2/3

Edwin
AnlytcPhil@aol.com