x^2+14x=-2

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Solution for x^2+14x=-2 equation: 


Simplifying
x2 + 14x = -2

Reorder the terms:
14x + x2 = -2

Solving
14x + x2 = -2

Solving for variable 'x'.

Reorder the terms:
2 + 14x + x2 = -2 + 2

Combine like terms: -2 + 2 = 0
2 + 14x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + 14x + -2 + x2 = 0 + -2

Reorder the terms:
2 + -2 + 14x + x2 = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 14x + x2 = 0 + -2
14x + x2 = 0 + -2

Combine like terms: 0 + -2 = -2
14x + x2 = -2

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 = -2 + 49

Reorder the terms:
49 + 14x + x2 = -2 + 49

Combine like terms: -2 + 49 = 47
49 + 14x + x2 = 47

Factor a perfect square on the left side:
(x + 7)(x + 7) = 47

Calculate the square root of the right side: 6.8556546

Break this problem into two subproblems by setting 
(x + 7) equal to 6.8556546 and -6.8556546.


Subproblem 1
x + 7 = 6.8556546

Simplifying
x + 7 = 6.8556546

Reorder the terms:
7 + x = 6.8556546

Solving
7 + x = 6.8556546

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 = 6.8556546 + -7

Combine like terms: 7 + -7 = 0
0 + x = 6.8556546 + -7
x = 6.8556546 + -7

Combine like terms: 6.8556546 + -7 = -0.1443454
x = -0.1443454

Simplifying
x = -0.1443454


Subproblem 2
x + 7 = -6.8556546

Simplifying
x + 7 = -6.8556546

Reorder the terms:
7 + x = -6.8556546

Solving
7 + x = -6.8556546

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 = -6.8556546 + -7

Combine like terms: 7 + -7 = 0
0 + x = -6.8556546 + -7
x = -6.8556546 + -7

Combine like terms: -6.8556546 + -7 = -13.8556546
x = -13.8556546

Simplifying
x = -13.8556546


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.1443454, -13.8556546}

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