6x^2+6x+11=3

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


Simplifying
6x2 + 6x + 11 = 3

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

Solving
11 + 6x + 6x2 = 3

Solving for variable 'x'.

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

Combine like terms: 11 + -3 = 8
8 + 6x + 6x2 = 3 + -3

Combine like terms: 3 + -3 = 0
8 + 6x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(4 + 3x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(4 + 3x + 3x2)' equal to zero and attempt to solve:

Simplifying
4 + 3x + 3x2 = 0

Solving
4 + 3x + 3x2 = 0

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

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

Move the constant term to the right:

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

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

Combine like terms: 1.333333333 + -1.333333333 = 0.000000000
0.000000000 + x + x2 = 0 + -1.333333333
x + x2 = 0 + -1.333333333

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

The x term is x.  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.
 + 0.25 + x2 = -1.333333333 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = -1.333333333 + 0.25

Combine like terms: -1.333333333 + 0.25 = -1.083333333
1.25 + x2 = -1.083333333

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = -1.083333333

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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