x^2+13.6x+28=0

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Solution for x^2+13.6x+28=0 equation: 


Simplifying
x2 + 13.6x + 28 = 0

Reorder the terms:
28 + 13.6x + x2 = 0

Solving
28 + 13.6x + 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 + 13.6x + -28 + x2 = 0 + -28

Reorder the terms:
28 + -28 + 13.6x + x2 = 0 + -28

Combine like terms: 28 + -28 = 0
0 + 13.6x + x2 = 0 + -28
13.6x + x2 = 0 + -28

Combine like terms: 0 + -28 = -28
13.6x + x2 = -28

The x term is 13.6x.  Take half its coefficient (6.8).
Square it (46.24) and add it to both sides.

Add '46.24' to each side of the equation.
13.6x + 46.24 + x2 = -28 + 46.24

Reorder the terms:
46.24 + 13.6x + x2 = -28 + 46.24

Combine like terms: -28 + 46.24 = 18.24
46.24 + 13.6x + x2 = 18.24

Factor a perfect square on the left side:
(x + 6.8)(x + 6.8) = 18.24

Calculate the square root of the right side: 4.270831301

Break this problem into two subproblems by setting 
(x + 6.8) equal to 4.270831301 and -4.270831301.


Subproblem 1
x + 6.8 = 4.270831301

Simplifying
x + 6.8 = 4.270831301

Reorder the terms:
6.8 + x = 4.270831301

Solving
6.8 + x = 4.270831301

Solving for variable 'x'.

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

Add '-6.8' to each side of the equation.
6.8 + -6.8 + x = 4.270831301 + -6.8

Combine like terms: 6.8 + -6.8 = 0.0
0.0 + x = 4.270831301 + -6.8
x = 4.270831301 + -6.8

Combine like terms: 4.270831301 + -6.8 = -2.529168699
x = -2.529168699

Simplifying
x = -2.529168699


Subproblem 2
x + 6.8 = -4.270831301

Simplifying
x + 6.8 = -4.270831301

Reorder the terms:
6.8 + x = -4.270831301

Solving
6.8 + x = -4.270831301

Solving for variable 'x'.

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

Add '-6.8' to each side of the equation.
6.8 + -6.8 + x = -4.270831301 + -6.8

Combine like terms: 6.8 + -6.8 = 0.0
0.0 + x = -4.270831301 + -6.8
x = -4.270831301 + -6.8

Combine like terms: -4.270831301 + -6.8 = -11.070831301
x = -11.070831301

Simplifying
x = -11.070831301


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-2.529168699, -11.070831301}

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