a^2+8a+5=0

Solution for a^2+8a+5=0 equation:

Simplifying
a2 + 8a + 5 = 0

Reorder the terms:
5 + 8a + a2 = 0

Solving
5 + 8a + 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 + 8a + -5 + a2 = 0 + -5

Reorder the terms:
5 + -5 + 8a + a2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 8a + a2 = 0 + -5
8a + a2 = 0 + -5

Combine like terms: 0 + -5 = -5
8a + a2 = -5

The a term is 8a.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8a + 16 + a2 = -5 + 16

Reorder the terms:
16 + 8a + a2 = -5 + 16

Combine like terms: -5 + 16 = 11
16 + 8a + a2 = 11

Factor a perfect square on the left side:
(a + 4)(a + 4) = 11

Calculate the square root of the right side: 3.31662479

Break this problem into two subproblems by setting 
(a + 4) equal to 3.31662479 and -3.31662479.

Subproblem 1
a + 4 = 3.31662479

Simplifying
a + 4 = 3.31662479

Reorder the terms:
4 + a = 3.31662479

Solving
4 + a = 3.31662479

Solving for variable 'a'.

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

Add '-4' to each side of the equation.
4 + -4 + a = 3.31662479 + -4

Combine like terms: 4 + -4 = 0
0 + a = 3.31662479 + -4
a = 3.31662479 + -4

Combine like terms: 3.31662479 + -4 = -0.68337521
a = -0.68337521

Simplifying
a = -0.68337521

Subproblem 2
a + 4 = -3.31662479

Simplifying
a + 4 = -3.31662479

Reorder the terms:
4 + a = -3.31662479

Solving
4 + a = -3.31662479

Solving for variable 'a'.

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

Add '-4' to each side of the equation.
4 + -4 + a = -3.31662479 + -4

Combine like terms: 4 + -4 = 0
0 + a = -3.31662479 + -4
a = -3.31662479 + -4

Combine like terms: -3.31662479 + -4 = -7.31662479
a = -7.31662479

Simplifying
a = -7.31662479

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {-0.68337521, -7.31662479}