Completing the Square

3x^2-2x-2=4    add 2 to both sides

3x^2 - 2x    =   6        divide every term by 3

x^2 - (2/3)x  =   2      take 1/2 of 2/3, square it and add to both sides

x^2  - (2/3)x + 1/9   = 2 + 1/9        factor the left side

( x  - 1/3)^2  =  19/9         take the squareroot of both sides

x - 1/3   = pos/neg sqrt(19)/2       add 1/3    to both sides

x =     pos/neg sqrt(19)   + 1/3

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