a^2+6a-56=0

Solution for a^2+6a-56=0 equation:

Simplifying
a2 + 6a + -56 = 0

Reorder the terms:
-56 + 6a + a2 = 0

Solving
-56 + 6a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '56' to each side of the equation.
-56 + 6a + 56 + a2 = 0 + 56

Reorder the terms:
-56 + 56 + 6a + a2 = 0 + 56

Combine like terms: -56 + 56 = 0
0 + 6a + a2 = 0 + 56
6a + a2 = 0 + 56

Combine like terms: 0 + 56 = 56
6a + a2 = 56

The a term is 6a.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6a + 9 + a2 = 56 + 9

Reorder the terms:
9 + 6a + a2 = 56 + 9

Combine like terms: 56 + 9 = 65
9 + 6a + a2 = 65

Factor a perfect square on the left side:
(a + 3)(a + 3) = 65

Calculate the square root of the right side: 8.062257748

Break this problem into two subproblems by setting 
(a + 3) equal to 8.062257748 and -8.062257748.

Subproblem 1
a + 3 = 8.062257748

Simplifying
a + 3 = 8.062257748

Reorder the terms:
3 + a = 8.062257748

Solving
3 + a = 8.062257748

Solving for variable 'a'.

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

Add '-3' to each side of the equation.
3 + -3 + a = 8.062257748 + -3

Combine like terms: 3 + -3 = 0
0 + a = 8.062257748 + -3
a = 8.062257748 + -3

Combine like terms: 8.062257748 + -3 = 5.062257748
a = 5.062257748

Simplifying
a = 5.062257748

Subproblem 2
a + 3 = -8.062257748

Simplifying
a + 3 = -8.062257748

Reorder the terms:
3 + a = -8.062257748

Solving
3 + a = -8.062257748

Solving for variable 'a'.

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

Add '-3' to each side of the equation.
3 + -3 + a = -8.062257748 + -3

Combine like terms: 3 + -3 = 0
0 + a = -8.062257748 + -3
a = -8.062257748 + -3

Combine like terms: -8.062257748 + -3 = -11.062257748
a = -11.062257748

Simplifying
a = -11.062257748

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {5.062257748, -11.062257748}