a^2+6a-5=0

Solution for a^2+6a-5=0 equation:

Simplifying
a2 + 6a + -5 = 0

Reorder the terms:
-5 + 6a + a2 = 0

Solving
-5 + 6a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + 6a + 5 + a2 = 0 + 5

Reorder the terms:
-5 + 5 + 6a + a2 = 0 + 5

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

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

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 = 5 + 9

Reorder the terms:
9 + 6a + a2 = 5 + 9

Combine like terms: 5 + 9 = 14
9 + 6a + a2 = 14

Factor a perfect square on the left side:
(a + 3)(a + 3) = 14

Calculate the square root of the right side: 3.741657387

Break this problem into two subproblems by setting 
(a + 3) equal to 3.741657387 and -3.741657387.

Subproblem 1
a + 3 = 3.741657387

Simplifying
a + 3 = 3.741657387

Reorder the terms:
3 + a = 3.741657387

Solving
3 + a = 3.741657387

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 = 3.741657387 + -3

Combine like terms: 3 + -3 = 0
0 + a = 3.741657387 + -3
a = 3.741657387 + -3

Combine like terms: 3.741657387 + -3 = 0.741657387
a = 0.741657387

Simplifying
a = 0.741657387

Subproblem 2
a + 3 = -3.741657387

Simplifying
a + 3 = -3.741657387

Reorder the terms:
3 + a = -3.741657387

Solving
3 + a = -3.741657387

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 = -3.741657387 + -3

Combine like terms: 3 + -3 = 0
0 + a = -3.741657387 + -3
a = -3.741657387 + -3

Combine like terms: -3.741657387 + -3 = -6.741657387
a = -6.741657387

Simplifying
a = -6.741657387

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {0.741657387, -6.741657387}