x^2+14x+28=0

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Solution for x^2+14x+28=0 equation: 


Simplifying
x2 + 14x + 28 = 0

Reorder the terms:
28 + 14x + x2 = 0

Solving
28 + 14x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-28' to each side of the equation.
28 + 14x + -28 + x2 = 0 + -28

Reorder the terms:
28 + -28 + 14x + x2 = 0 + -28

Combine like terms: 28 + -28 = 0
0 + 14x + x2 = 0 + -28
14x + x2 = 0 + -28

Combine like terms: 0 + -28 = -28
14x + x2 = -28

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 = -28 + 49

Reorder the terms:
49 + 14x + x2 = -28 + 49

Combine like terms: -28 + 49 = 21
49 + 14x + x2 = 21

Factor a perfect square on the left side:
(x + 7)(x + 7) = 21

Calculate the square root of the right side: 4.582575695

Break this problem into two subproblems by setting 
(x + 7) equal to 4.582575695 and -4.582575695.


Subproblem 1
x + 7 = 4.582575695

Simplifying
x + 7 = 4.582575695

Reorder the terms:
7 + x = 4.582575695

Solving
7 + x = 4.582575695

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 = 4.582575695 + -7

Combine like terms: 7 + -7 = 0
0 + x = 4.582575695 + -7
x = 4.582575695 + -7

Combine like terms: 4.582575695 + -7 = -2.417424305
x = -2.417424305

Simplifying
x = -2.417424305


Subproblem 2
x + 7 = -4.582575695

Simplifying
x + 7 = -4.582575695

Reorder the terms:
7 + x = -4.582575695

Solving
7 + x = -4.582575695

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 = -4.582575695 + -7

Combine like terms: 7 + -7 = 0
0 + x = -4.582575695 + -7
x = -4.582575695 + -7

Combine like terms: -4.582575695 + -7 = -11.582575695
x = -11.582575695

Simplifying
x = -11.582575695


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-2.417424305, -11.582575695}

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