-2a^2-6a=1

Solution for -2a^2-6a=1 equation:

Simplifying
-2a2 + -6a = 1

Reorder the terms:
-6a + -2a2 = 1

Solving
-6a + -2a2 = 1

Solving for variable 'a'.

Reorder the terms:
-1 + -6a + -2a2 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + -6a + -2a2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(1 + 6a + 2a2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(1 + 6a + 2a2)' equal to zero and attempt to solve:

Simplifying
1 + 6a + 2a2 = 0

Solving
1 + 6a + 2a2 = 0

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

Divide each side by '2'.
0.5 + 3a + a2 = 0

Move the constant term to the right:

Add '-0.5' to each side of the equation.
0.5 + 3a + -0.5 + a2 = 0 + -0.5

Reorder the terms:
0.5 + -0.5 + 3a + a2 = 0 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + 3a + a2 = 0 + -0.5
3a + a2 = 0 + -0.5

Combine like terms: 0 + -0.5 = -0.5
3a + a2 = -0.5

The a term is 3a.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3a + 2.25 + a2 = -0.5 + 2.25

Reorder the terms:
2.25 + 3a + a2 = -0.5 + 2.25

Combine like terms: -0.5 + 2.25 = 1.75
2.25 + 3a + a2 = 1.75

Factor a perfect square on the left side:
(a + 1.5)(a + 1.5) = 1.75

Calculate the square root of the right side: 1.322875656

Break this problem into two subproblems by setting 
(a + 1.5) equal to 1.322875656 and -1.322875656.

Subproblem 1
a + 1.5 = 1.322875656

Simplifying
a + 1.5 = 1.322875656

Reorder the terms:
1.5 + a = 1.322875656

Solving
1.5 + a = 1.322875656

Solving for variable 'a'.

Move all terms containing a to the left, all other terms to the right.

Add '-1.5' to each side of the equation.
1.5 + -1.5 + a = 1.322875656 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + a = 1.322875656 + -1.5
a = 1.322875656 + -1.5

Combine like terms: 1.322875656 + -1.5 = -0.177124344
a = -0.177124344

Simplifying
a = -0.177124344

Subproblem 2
a + 1.5 = -1.322875656

Simplifying
a + 1.5 = -1.322875656

Reorder the terms:
1.5 + a = -1.322875656

Solving
1.5 + a = -1.322875656

Solving for variable 'a'.

Move all terms containing a to the left, all other terms to the right.

Add '-1.5' to each side of the equation.
1.5 + -1.5 + a = -1.322875656 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + a = -1.322875656 + -1.5
a = -1.322875656 + -1.5

Combine like terms: -1.322875656 + -1.5 = -2.822875656
a = -2.822875656

Simplifying
a = -2.822875656

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {-0.177124344, -2.822875656}
Solution
a = {-0.177124344, -2.822875656}