a^2+13a+13=0

Solution for a^2+13a+13=0 equation:

Simplifying
a2 + 13a + 13 = 0

Reorder the terms:
13 + 13a + a2 = 0

Solving
13 + 13a + a2 = 0

Solving for variable 'a'.

Begin completing the square.

Move the constant term to the right:

Add '-13' to each side of the equation.
13 + 13a + -13 + a2 = 0 + -13

Reorder the terms:
13 + -13 + 13a + a2 = 0 + -13

Combine like terms: 13 + -13 = 0
0 + 13a + a2 = 0 + -13
13a + a2 = 0 + -13

Combine like terms: 0 + -13 = -13
13a + a2 = -13

The a term is 13a.  Take half its coefficient (6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
13a + 42.25 + a2 = -13 + 42.25

Reorder the terms:
42.25 + 13a + a2 = -13 + 42.25

Combine like terms: -13 + 42.25 = 29.25
42.25 + 13a + a2 = 29.25

Factor a perfect square on the left side:
(a + 6.5)(a + 6.5) = 29.25

Calculate the square root of the right side: 5.408326913

Break this problem into two subproblems by setting 
(a + 6.5) equal to 5.408326913 and -5.408326913.

Subproblem 1
a + 6.5 = 5.408326913

Simplifying
a + 6.5 = 5.408326913

Reorder the terms:
6.5 + a = 5.408326913

Solving
6.5 + a = 5.408326913

Solving for variable 'a'.

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

Add '-6.5' to each side of the equation.
6.5 + -6.5 + a = 5.408326913 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + a = 5.408326913 + -6.5
a = 5.408326913 + -6.5

Combine like terms: 5.408326913 + -6.5 = -1.091673087
a = -1.091673087

Simplifying
a = -1.091673087

Subproblem 2
a + 6.5 = -5.408326913

Simplifying
a + 6.5 = -5.408326913

Reorder the terms:
6.5 + a = -5.408326913

Solving
6.5 + a = -5.408326913

Solving for variable 'a'.

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

Add '-6.5' to each side of the equation.
6.5 + -6.5 + a = -5.408326913 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + a = -5.408326913 + -6.5
a = -5.408326913 + -6.5

Combine like terms: -5.408326913 + -6.5 = -11.908326913
a = -11.908326913

Simplifying
a = -11.908326913

Solution
The solution to the problem is based on the solutions
from the subproblems.
a = {-1.091673087, -11.908326913}