3a^2+6a+2=0

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Solution for 3a^2+6a+2=0 equation:


Simplifying
3a2 + 6a + 2 = 0

Reorder the terms:
2 + 6a + 3a2 = 0

Solving
2 + 6a + 3a2 = 0

Solving for variable 'a'.

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

Divide each side by '3'.
0.6666666667 + 2a + a2 = 0

Move the constant term to the right:

Add '-0.6666666667' to each side of the equation.
0.6666666667 + 2a + -0.6666666667 + a2 = 0 + -0.6666666667

Reorder the terms:
0.6666666667 + -0.6666666667 + 2a + a2 = 0 + -0.6666666667

Combine like terms: 0.6666666667 + -0.6666666667 = 0.0000000000
0.0000000000 + 2a + a2 = 0 + -0.6666666667
2a + a2 = 0 + -0.6666666667

Combine like terms: 0 + -0.6666666667 = -0.6666666667
2a + a2 = -0.6666666667

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

Add '1' to each side of the equation.
2a + 1 + a2 = -0.6666666667 + 1

Reorder the terms:
1 + 2a + a2 = -0.6666666667 + 1

Combine like terms: -0.6666666667 + 1 = 0.3333333333
1 + 2a + a2 = 0.3333333333

Factor a perfect square on the left side:
(a + 1)(a + 1) = 0.3333333333

Calculate the square root of the right side: 0.577350269

Break this problem into two subproblems by setting 
(a + 1) equal to 0.577350269 and -0.577350269.

Subproblem 1

a + 1 = 0.577350269 Simplifying a + 1 = 0.577350269 Reorder the terms: 1 + a = 0.577350269 Solving 1 + a = 0.577350269 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + a = 0.577350269 + -1 Combine like terms: 1 + -1 = 0 0 + a = 0.577350269 + -1 a = 0.577350269 + -1 Combine like terms: 0.577350269 + -1 = -0.422649731 a = -0.422649731 Simplifying a = -0.422649731

Subproblem 2

a + 1 = -0.577350269 Simplifying a + 1 = -0.577350269 Reorder the terms: 1 + a = -0.577350269 Solving 1 + a = -0.577350269 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + a = -0.577350269 + -1 Combine like terms: 1 + -1 = 0 0 + a = -0.577350269 + -1 a = -0.577350269 + -1 Combine like terms: -0.577350269 + -1 = -1.577350269 a = -1.577350269 Simplifying a = -1.577350269

Solution

The solution to the problem is based on the solutions from the subproblems. a = {-0.422649731, -1.577350269}

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