a^2+6a=1-a

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

Simplifying
a2 + 6a = 1 + -1a

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

Solving
6a + a2 = 1 + -1a

Solving for variable 'a'.

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

Combine like terms: 6a + a = 7a
-1 + 7a + a2 = 1 + -1a + -1 + a

Reorder the terms:
-1 + 7a + a2 = 1 + -1 + -1a + a

Combine like terms: 1 + -1 = 0
-1 + 7a + a2 = 0 + -1a + a
-1 + 7a + a2 = -1a + a

Combine like terms: -1a + a = 0
-1 + 7a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 7a + 1 + a2 = 0 + 1

Reorder the terms:
-1 + 1 + 7a + a2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 7a + a2 = 0 + 1
7a + a2 = 0 + 1

Combine like terms: 0 + 1 = 1
7a + a2 = 1

The a term is 7a.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7a + 12.25 + a2 = 1 + 12.25

Reorder the terms:
12.25 + 7a + a2 = 1 + 12.25

Combine like terms: 1 + 12.25 = 13.25
12.25 + 7a + a2 = 13.25

Factor a perfect square on the left side:
(a + 3.5)(a + 3.5) = 13.25

Calculate the square root of the right side: 3.640054945

Break this problem into two subproblems by setting 
(a + 3.5) equal to 3.640054945 and -3.640054945.

Subproblem 1
a + 3.5 = 3.640054945

Simplifying
a + 3.5 = 3.640054945

Reorder the terms:
3.5 + a = 3.640054945

Solving
3.5 + a = 3.640054945

Solving for variable 'a'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + a = 3.640054945 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + a = 3.640054945 + -3.5
a = 3.640054945 + -3.5

Combine like terms: 3.640054945 + -3.5 = 0.140054945
a = 0.140054945

Simplifying
a = 0.140054945

Subproblem 2
a + 3.5 = -3.640054945

Simplifying
a + 3.5 = -3.640054945

Reorder the terms:
3.5 + a = -3.640054945

Solving
3.5 + a = -3.640054945

Solving for variable 'a'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + a = -3.640054945 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + a = -3.640054945 + -3.5
a = -3.640054945 + -3.5

Combine like terms: -3.640054945 + -3.5 = -7.140054945
a = -7.140054945

Simplifying
a = -7.140054945

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {0.140054945, -7.140054945}