x^2+14x+18=0

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Solution for x^2+14x+18=0 equation: 


Simplifying
x2 + 14x + 18 = 0

Reorder the terms:
18 + 14x + x2 = 0

Solving
18 + 14x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-18' to each side of the equation.
18 + 14x + -18 + x2 = 0 + -18

Reorder the terms:
18 + -18 + 14x + x2 = 0 + -18

Combine like terms: 18 + -18 = 0
0 + 14x + x2 = 0 + -18
14x + x2 = 0 + -18

Combine like terms: 0 + -18 = -18
14x + x2 = -18

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 = -18 + 49

Reorder the terms:
49 + 14x + x2 = -18 + 49

Combine like terms: -18 + 49 = 31
49 + 14x + x2 = 31

Factor a perfect square on the left side:
(x + 7)(x + 7) = 31

Calculate the square root of the right side: 5.567764363

Break this problem into two subproblems by setting 
(x + 7) equal to 5.567764363 and -5.567764363.


Subproblem 1
x + 7 = 5.567764363

Simplifying
x + 7 = 5.567764363

Reorder the terms:
7 + x = 5.567764363

Solving
7 + x = 5.567764363

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 = 5.567764363 + -7

Combine like terms: 7 + -7 = 0
0 + x = 5.567764363 + -7
x = 5.567764363 + -7

Combine like terms: 5.567764363 + -7 = -1.432235637
x = -1.432235637

Simplifying
x = -1.432235637


Subproblem 2
x + 7 = -5.567764363

Simplifying
x + 7 = -5.567764363

Reorder the terms:
7 + x = -5.567764363

Solving
7 + x = -5.567764363

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 = -5.567764363 + -7

Combine like terms: 7 + -7 = 0
0 + x = -5.567764363 + -7
x = -5.567764363 + -7

Combine like terms: -5.567764363 + -7 = -12.567764363
x = -12.567764363

Simplifying
x = -12.567764363


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.432235637, -12.567764363}

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