a^2+5a+5=0

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


Simplifying
a2 + 5a + 5 = 0

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

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

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

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

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

The a term is 5a.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5a + 6.25 + a2 = -5 + 6.25

Reorder the terms:
6.25 + 5a + a2 = -5 + 6.25

Combine like terms: -5 + 6.25 = 1.25
6.25 + 5a + a2 = 1.25

Factor a perfect square on the left side:
(a + 2.5)(a + 2.5) = 1.25

Calculate the square root of the right side: 1.118033989

Break this problem into two subproblems by setting 
(a + 2.5) equal to 1.118033989 and -1.118033989.


Subproblem 1
a + 2.5 = 1.118033989

Simplifying
a + 2.5 = 1.118033989

Reorder the terms:
2.5 + a = 1.118033989

Solving
2.5 + a = 1.118033989

Solving for variable 'a'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + a = 1.118033989 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + a = 1.118033989 + -2.5
a = 1.118033989 + -2.5

Combine like terms: 1.118033989 + -2.5 = -1.381966011
a = -1.381966011

Simplifying
a = -1.381966011


Subproblem 2
a + 2.5 = -1.118033989

Simplifying
a + 2.5 = -1.118033989

Reorder the terms:
2.5 + a = -1.118033989

Solving
2.5 + a = -1.118033989

Solving for variable 'a'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + a = -1.118033989 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + a = -1.118033989 + -2.5
a = -1.118033989 + -2.5

Combine like terms: -1.118033989 + -2.5 = -3.618033989
a = -3.618033989

Simplifying
a = -3.618033989


Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {-1.381966011, -3.618033989}

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