3x^2=6x-11

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Solution for 3x^2=6x-11 equation: 


Simplifying
3x2 = 6x + -11

Reorder the terms:
3x2 = -11 + 6x

Solving
3x2 = -11 + 6x

Solving for variable 'x'.

Reorder the terms:
11 + -6x + 3x2 = -11 + 6x + 11 + -6x

Reorder the terms:
11 + -6x + 3x2 = -11 + 11 + 6x + -6x

Combine like terms: -11 + 11 = 0
11 + -6x + 3x2 = 0 + 6x + -6x
11 + -6x + 3x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
11 + -6x + 3x2 = 0

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

Divide each side by '3'.
3.666666667 + -2x + x2 = 0

Move the constant term to the right:

Add '-3.666666667' to each side of the equation.
3.666666667 + -2x + -3.666666667 + x2 = 0 + -3.666666667

Reorder the terms:
3.666666667 + -3.666666667 + -2x + x2 = 0 + -3.666666667

Combine like terms: 3.666666667 + -3.666666667 = 0.000000000
0.000000000 + -2x + x2 = 0 + -3.666666667
-2x + x2 = 0 + -3.666666667

Combine like terms: 0 + -3.666666667 = -3.666666667
-2x + x2 = -3.666666667

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = -3.666666667 + 1

Reorder the terms:
1 + -2x + x2 = -3.666666667 + 1

Combine like terms: -3.666666667 + 1 = -2.666666667
1 + -2x + x2 = -2.666666667

Factor a perfect square on the left side:
(x + -1)(x + -1) = -2.666666667

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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