2x-6=3x^2-4

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Solution for 2x-6=3x^2-4 equation: 


Simplifying
2x + -6 = 3x2 + -4

Reorder the terms:
-6 + 2x = 3x2 + -4

Reorder the terms:
-6 + 2x = -4 + 3x2

Solving
-6 + 2x = -4 + 3x2

Solving for variable 'x'.

Reorder the terms:
-6 + 4 + 2x + -3x2 = -4 + 3x2 + 4 + -3x2

Combine like terms: -6 + 4 = -2
-2 + 2x + -3x2 = -4 + 3x2 + 4 + -3x2

Reorder the terms:
-2 + 2x + -3x2 = -4 + 4 + 3x2 + -3x2

Combine like terms: -4 + 4 = 0
-2 + 2x + -3x2 = 0 + 3x2 + -3x2
-2 + 2x + -3x2 = 3x2 + -3x2

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

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

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

Move the constant term to the right:

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

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

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

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

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 = -0.6666666667 + 0.1111111112

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

Combine like terms: -0.6666666667 + 0.1111111112 = -0.5555555555
0.1111111112 + -0.6666666667x + x2 = -0.5555555555

Factor a perfect square on the left side:
(x + -0.3333333334)(x + -0.3333333334) = -0.5555555555

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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