x^2+14x+38=0

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Solution for x^2+14x+38=0 equation: 


Simplifying
x2 + 14x + 38 = 0

Reorder the terms:
38 + 14x + x2 = 0

Solving
38 + 14x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-38' to each side of the equation.
38 + 14x + -38 + x2 = 0 + -38

Reorder the terms:
38 + -38 + 14x + x2 = 0 + -38

Combine like terms: 38 + -38 = 0
0 + 14x + x2 = 0 + -38
14x + x2 = 0 + -38

Combine like terms: 0 + -38 = -38
14x + x2 = -38

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 = -38 + 49

Reorder the terms:
49 + 14x + x2 = -38 + 49

Combine like terms: -38 + 49 = 11
49 + 14x + x2 = 11

Factor a perfect square on the left side:
(x + 7)(x + 7) = 11

Calculate the square root of the right side: 3.31662479

Break this problem into two subproblems by setting 
(x + 7) equal to 3.31662479 and -3.31662479.


Subproblem 1
x + 7 = 3.31662479

Simplifying
x + 7 = 3.31662479

Reorder the terms:
7 + x = 3.31662479

Solving
7 + x = 3.31662479

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 = 3.31662479 + -7

Combine like terms: 7 + -7 = 0
0 + x = 3.31662479 + -7
x = 3.31662479 + -7

Combine like terms: 3.31662479 + -7 = -3.68337521
x = -3.68337521

Simplifying
x = -3.68337521


Subproblem 2
x + 7 = -3.31662479

Simplifying
x + 7 = -3.31662479

Reorder the terms:
7 + x = -3.31662479

Solving
7 + x = -3.31662479

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 = -3.31662479 + -7

Combine like terms: 7 + -7 = 0
0 + x = -3.31662479 + -7
x = -3.31662479 + -7

Combine like terms: -3.31662479 + -7 = -10.31662479
x = -10.31662479

Simplifying
x = -10.31662479


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-3.68337521, -10.31662479}

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