Math question: Solve by square root method

2x^2 - 3x + 1 = 0        I think you mean "Completing the Square"  method

Divide through by 2, the lead coefficient 

x^2  - (3/2)x  + 1/2   = 0    subtract 1/2 from each side

x^2 - (3/2)x   =  -1/2         take !/2 of (3/2)   =  3/4  ....square this   =  9/16   and add to both sides

x^2 - (3/2)  + 9/16   = -1/2 + 9/16

x^2  - (3/2)x  + 9/16  = 1/16   factor the left side

[ x  - 3/4] ^2   = 1/16       take the square root of both side

x -3/4  = ± √ (1/16)

x - 3/4  =  ± (1/4)    add 3/4 to both sides

x  = ± (1/4)  + 3/4

x = 1/4 + 3/4   = 1      ...   or   ....   x  = -1/4 + 3/4  =  2/4  = 1/2