x^2+14x+1=0

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Solution for x^2+14x+1=0 equation: 


Simplifying
x2 + 14x + 1 = 0

Reorder the terms:
1 + 14x + x2 = 0

Solving
1 + 14x + 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 + 14x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + 14x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 14x + x2 = 0 + -1
14x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
14x + x2 = -1

The x term is 14x.  Take half its coefficient (7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
14x + 49 + x2 = -1 + 49

Reorder the terms:
49 + 14x + x2 = -1 + 49

Combine like terms: -1 + 49 = 48
49 + 14x + x2 = 48

Factor a perfect square on the left side:
(x + 7)(x + 7) = 48

Calculate the square root of the right side: 6.92820323

Break this problem into two subproblems by setting 
(x + 7) equal to 6.92820323 and -6.92820323.


Subproblem 1
x + 7 = 6.92820323

Simplifying
x + 7 = 6.92820323

Reorder the terms:
7 + x = 6.92820323

Solving
7 + x = 6.92820323

Solving for variable 'x'.

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

Add '-7' to each side of the equation.
7 + -7 + x = 6.92820323 + -7

Combine like terms: 7 + -7 = 0
0 + x = 6.92820323 + -7
x = 6.92820323 + -7

Combine like terms: 6.92820323 + -7 = -0.07179677
x = -0.07179677

Simplifying
x = -0.07179677


Subproblem 2
x + 7 = -6.92820323

Simplifying
x + 7 = -6.92820323

Reorder the terms:
7 + x = -6.92820323

Solving
7 + x = -6.92820323

Solving for variable 'x'.

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

Add '-7' to each side of the equation.
7 + -7 + x = -6.92820323 + -7

Combine like terms: 7 + -7 = 0
0 + x = -6.92820323 + -7
x = -6.92820323 + -7

Combine like terms: -6.92820323 + -7 = -13.92820323
x = -13.92820323

Simplifying
x = -13.92820323


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.07179677, -13.92820323}

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