3x^2-3x+5=x+2

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Solution for 3x^2-3x+5=x+2 equation: 


Simplifying
3x2 + -3x + 5 = x + 2

Reorder the terms:
5 + -3x + 3x2 = x + 2

Reorder the terms:
5 + -3x + 3x2 = 2 + x

Solving
5 + -3x + 3x2 = 2 + x

Solving for variable 'x'.

Reorder the terms:
5 + -2 + -3x + -1x + 3x2 = 2 + x + -2 + -1x

Combine like terms: 5 + -2 = 3
3 + -3x + -1x + 3x2 = 2 + x + -2 + -1x

Combine like terms: -3x + -1x = -4x
3 + -4x + 3x2 = 2 + x + -2 + -1x

Reorder the terms:
3 + -4x + 3x2 = 2 + -2 + x + -1x

Combine like terms: 2 + -2 = 0
3 + -4x + 3x2 = 0 + x + -1x
3 + -4x + 3x2 = x + -1x

Combine like terms: x + -1x = 0
3 + -4x + 3x2 = 0

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

Divide each side by '3'.
1 + -1.333333333x + x2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -1.333333333x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + -1.333333333x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1.333333333x + x2 = 0 + -1
-1.333333333x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
-1.333333333x + x2 = -1

The x term is -1.333333333x.  Take half its coefficient (-0.6666666665).
Square it (0.4444444442) and add it to both sides.

Add '0.4444444442' to each side of the equation.
-1.333333333x + 0.4444444442 + x2 = -1 + 0.4444444442

Reorder the terms:
0.4444444442 + -1.333333333x + x2 = -1 + 0.4444444442

Combine like terms: -1 + 0.4444444442 = -0.5555555558
0.4444444442 + -1.333333333x + x2 = -0.5555555558

Factor a perfect square on the left side:
(x + -0.6666666665)(x + -0.6666666665) = -0.5555555558

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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