6x^2+6x+10=0

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Solution for 6x^2+6x+10=0 equation: 


Simplifying
6x2 + 6x + 10 = 0

Reorder the terms:
10 + 6x + 6x2 = 0

Solving
10 + 6x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + 3x + 3x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(5 + 3x + 3x2)' equal to zero and attempt to solve:

Simplifying
5 + 3x + 3x2 = 0

Solving
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 + x + x2 = 0

Move the constant term to the right:

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

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

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

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

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 = -1.666666667 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = -1.666666667 + 0.25

Combine like terms: -1.666666667 + 0.25 = -1.416666667
1.25 + 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.

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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