3x^2=2x-1

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Solution for 3x^2=2x-1 equation: 


Simplifying
3x2 = 2x + -1

Reorder the terms:
3x2 = -1 + 2x

Solving
3x2 = -1 + 2x

Solving for variable 'x'.

Reorder the terms:
1 + -2x + 3x2 = -1 + 2x + 1 + -2x

Reorder the terms:
1 + -2x + 3x2 = -1 + 1 + 2x + -2x

Combine like terms: -1 + 1 = 0
1 + -2x + 3x2 = 0 + 2x + -2x
1 + -2x + 3x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
1 + -2x + 3x2 = 0

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
0.3333333333 + -0.6666666667x + x2 = 0

Move the constant term to the right:

Add '-0.3333333333' to each side of the equation.
0.3333333333 + -0.6666666667x + -0.3333333333 + x2 = 0 + -0.3333333333

Reorder the terms:
0.3333333333 + -0.3333333333 + -0.6666666667x + x2 = 0 + -0.3333333333

Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000
0.0000000000 + -0.6666666667x + x2 = 0 + -0.3333333333
-0.6666666667x + x2 = 0 + -0.3333333333

Combine like terms: 0 + -0.3333333333 = -0.3333333333
-0.6666666667x + x2 = -0.3333333333

The x term is -0.6666666667x.  Take half its coefficient (-0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
-0.6666666667x + 0.1111111112 + x2 = -0.3333333333 + 0.1111111112

Reorder the terms:
0.1111111112 + -0.6666666667x + x2 = -0.3333333333 + 0.1111111112

Combine like terms: -0.3333333333 + 0.1111111112 = -0.2222222221
0.1111111112 + -0.6666666667x + x2 = -0.2222222221

Factor a perfect square on the left side:
(x + -0.3333333334)(x + -0.3333333334) = -0.2222222221

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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