Solving these quadratics for x using complete the square 3x^2-4x-1=0. Show your work.

x = (sqrt(7) + 2)/3 and
x = ( – sqrt(7) + 2)/3

Explanation:

3x^2 - 4x - 1 = 0

Divide both sides by 3:

3x^2/3 - 4/3x - 1/3 = 0/3
x^2 - 4/3x - 1/3 = 0
x^2 - 4/3x = 1/3
x^2 - 4/3x + (2/3)^2 = 1/3 + (2/3)^2
(x - 2/3)^2 = 1/3 + 4/9
(x - 2/3)^2 = 7/9

Sqrt both sides:

x - 2/3 = sqrt (7/9)
x - 2/3 = |sqrt(7)/3|

Set x -2/3 = sqrt(7)/3

=> x = (sqrt(7) + 2)/3

Set x - 2/3 = - sqrt(7)/3

=> x = ( - sqrt(7) + 2)/3

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