18a^2+2a+6=0

Solution for 18a^2+2a+6=0 equation:

Simplifying
18a2 + 2a + 6 = 0

Reorder the terms:
6 + 2a + 18a2 = 0

Solving
6 + 2a + 18a2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + a + 9a2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + a + 9a2)' equal to zero and attempt to solve:

Simplifying
3 + a + 9a2 = 0

Solving
3 + a + 9a2 = 0

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

Divide each side by '9'.
0.3333333333 + 0.1111111111a + a2 = 0

Move the constant term to the right:

Add '-0.3333333333' to each side of the equation.
0.3333333333 + 0.1111111111a + -0.3333333333 + a2 = 0 + -0.3333333333

Reorder the terms:
0.3333333333 + -0.3333333333 + 0.1111111111a + a2 = 0 + -0.3333333333

Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000
0.0000000000 + 0.1111111111a + a2 = 0 + -0.3333333333
0.1111111111a + a2 = 0 + -0.3333333333

Combine like terms: 0 + -0.3333333333 = -0.3333333333
0.1111111111a + a2 = -0.3333333333

The a term is a.  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.
0.1111111111a + 0.25 + a2 = -0.3333333333 + 0.25

Reorder the terms:
0.25 + 0.1111111111a + a2 = -0.3333333333 + 0.25

Combine like terms: -0.3333333333 + 0.25 = -0.0833333333
0.25 + 0.1111111111a + a2 = -0.0833333333

Factor a perfect square on the left side:
(a + 0.5)(a + 0.5) = -0.0833333333

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.