Solve the equation 3x2 - 4x + 1 = 0

First you must make the coefficient of the x2 term into a 1.

    (1/3)(3x2 - 4x + 1) = (1/3)0

    x2 - (4/3)x + 1/3 = 0

Next we group the x and x2 terms together to get:

    (x2 - (4/3)x) + 1/3 = 0

Now we take the coefficient of the x term, divide it by 2 and then square that answer. Then we add and subtract that term.
    (x2 - (4/3)x + (-2/3)2) - (-2/3)2 + 1/3 = 0

    (x - 2/3)2 - 4/9 + 1/3 = 0

    (x - 2/3)2 - 1/9 = 0

    (x - 2/3)2 = 1/9

    x - 2/3 = 1/3 or x - 2/3 = -1/3

    x = 1 or x = 1/3

You can check your answer by substituting these values in for x in the original equation.

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