x^2+13x+1=0

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Solution for x^2+13x+1=0 equation:


Simplifying
x2 + 13x + 1 = 0

Reorder the terms:
1 + 13x + x2 = 0

Solving
1 + 13x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 13x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + 13x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 13x + x2 = 0 + -1
13x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
13x + x2 = -1

The x term is 13x.  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.
13x + 42.25 + x2 = -1 + 42.25

Reorder the terms:
42.25 + 13x + x2 = -1 + 42.25

Combine like terms: -1 + 42.25 = 41.25
42.25 + 13x + x2 = 41.25

Factor a perfect square on the left side:
(x + 6.5)(x + 6.5) = 41.25

Calculate the square root of the right side: 6.422616289

Break this problem into two subproblems by setting 
(x + 6.5) equal to 6.422616289 and -6.422616289.


Subproblem 1
x + 6.5 = 6.422616289

Simplifying
x + 6.5 = 6.422616289

Reorder the terms:
6.5 + x = 6.422616289

Solving
6.5 + x = 6.422616289

Solving for variable 'x'.

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

Add '-6.5' to each side of the equation.
6.5 + -6.5 + x = 6.422616289 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + x = 6.422616289 + -6.5
x = 6.422616289 + -6.5

Combine like terms: 6.422616289 + -6.5 = -0.077383711
x = -0.077383711

Simplifying
x = -0.077383711


Subproblem 2
x + 6.5 = -6.422616289

Simplifying
x + 6.5 = -6.422616289

Reorder the terms:
6.5 + x = -6.422616289

Solving
6.5 + x = -6.422616289

Solving for variable 'x'.

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

Add '-6.5' to each side of the equation.
6.5 + -6.5 + x = -6.422616289 + -6.5

Combine like terms: 6.5 + -6.5 = 0.0
0.0 + x = -6.422616289 + -6.5
x = -6.422616289 + -6.5

Combine like terms: -6.422616289 + -6.5 = -12.922616289
x = -12.922616289

Simplifying
x = -12.922616289


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.077383711, -12.922616289}

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