3x^2=3x-5

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


Simplifying
3x2 = 3x + -5

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

Solving
3x2 = -5 + 3x

Solving for variable 'x'.

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

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

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

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

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

Divide each side by '3'.
1.666666667 + -1x + x2 = 0

Move the constant term to the right:

Add '-1.666666667' to each side of the equation.
1.666666667 + -1x + -1.666666667 + x2 = 0 + -1.666666667

Reorder the terms:
1.666666667 + -1.666666667 + -1x + x2 = 0 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + -1x + x2 = 0 + -1.666666667
-1x + x2 = 0 + -1.666666667

Combine like terms: 0 + -1.666666667 = -1.666666667
-1x + x2 = -1.666666667

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = -1.666666667 + 0.25

Reorder the terms:
0.25 + -1x + x2 = -1.666666667 + 0.25

Combine like terms: -1.666666667 + 0.25 = -1.416666667
0.25 + -1x + x2 = -1.416666667

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = -1.416666667

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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