2+4a+4+a^2+2a+5a^2+3=

Solution for 2+4a+4+a^2+2a+5a^2+3= equation:

Simplifying
2 + 4a + 4 + a2 + 2a + 5a2 + 3 = 0

Reorder the terms:
2 + 4 + 3 + 4a + 2a + a2 + 5a2 = 0

Combine like terms: 2 + 4 = 6
6 + 3 + 4a + 2a + a2 + 5a2 = 0

Combine like terms: 6 + 3 = 9
9 + 4a + 2a + a2 + 5a2 = 0

Combine like terms: 4a + 2a = 6a
9 + 6a + a2 + 5a2 = 0

Combine like terms: a2 + 5a2 = 6a2
9 + 6a + 6a2 = 0

Solving
9 + 6a + 6a2 = 0

Solving for variable 'a'.

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

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

Simplifying
3 + 2a + 2a2 = 0

Solving
3 + 2a + 2a2 = 0

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

Divide each side by '2'.
1.5 + a + a2 = 0

Move the constant term to the right:

Add '-1.5' to each side of the equation.
1.5 + a + -1.5 + a2 = 0 + -1.5

Reorder the terms:
1.5 + -1.5 + a + a2 = 0 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + a + a2 = 0 + -1.5
a + a2 = 0 + -1.5

Combine like terms: 0 + -1.5 = -1.5
a + a2 = -1.5

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.
 + 0.25 + a2 = -1.5 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + a2 = -1.5 + 0.25

Combine like terms: -1.5 + 0.25 = -1.25
1.25 + a2 = -1.25

Factor a perfect square on the left side:
(a + 0.5)(a + 0.5) = -1.25

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.