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

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


Simplifying
-3x2 + -1x + 3x = 5

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

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

Solving
2x + -3x2 = 5

Solving for variable 'x'.

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

Combine like terms: 5 + -5 = 0
-5 + 2x + -3x2 = 0

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

Divide each side by '-3'.
1.666666667 + -0.6666666667x + x2 = 0

Move the constant term to the right:

Add '-1.666666667' to each side of the equation.
1.666666667 + -0.6666666667x + -1.666666667 + x2 = 0 + -1.666666667

Reorder the terms:
1.666666667 + -1.666666667 + -0.6666666667x + x2 = 0 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + -0.6666666667x + x2 = 0 + -1.666666667
-0.6666666667x + x2 = 0 + -1.666666667

Combine like terms: 0 + -1.666666667 = -1.666666667
-0.6666666667x + x2 = -1.666666667

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 = -1.666666667 + 0.1111111112

Reorder the terms:
0.1111111112 + -0.6666666667x + x2 = -1.666666667 + 0.1111111112

Combine like terms: -1.666666667 + 0.1111111112 = -1.5555555558
0.1111111112 + -0.6666666667x + x2 = -1.5555555558

Factor a perfect square on the left side:
(x + -0.3333333334)(x + -0.3333333334) = -1.5555555558

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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