x^2+10.8x-106.54=0

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Solution for x^2+10.8x-106.54=0 equation: 


Simplifying
x2 + 10.8x + -106.54 = 0

Reorder the terms:
-106.54 + 10.8x + x2 = 0

Solving
-106.54 + 10.8x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '106.54' to each side of the equation.
-106.54 + 10.8x + 106.54 + x2 = 0 + 106.54

Reorder the terms:
-106.54 + 106.54 + 10.8x + x2 = 0 + 106.54

Combine like terms: -106.54 + 106.54 = 0.00
0.00 + 10.8x + x2 = 0 + 106.54
10.8x + x2 = 0 + 106.54

Combine like terms: 0 + 106.54 = 106.54
10.8x + x2 = 106.54

The x term is 10.8x.  Take half its coefficient (5.4).
Square it (29.16) and add it to both sides.

Add '29.16' to each side of the equation.
10.8x + 29.16 + x2 = 106.54 + 29.16

Reorder the terms:
29.16 + 10.8x + x2 = 106.54 + 29.16

Combine like terms: 106.54 + 29.16 = 135.7
29.16 + 10.8x + x2 = 135.7

Factor a perfect square on the left side:
(x + 5.4)(x + 5.4) = 135.7

Calculate the square root of the right side: 11.649034295

Break this problem into two subproblems by setting 
(x + 5.4) equal to 11.649034295 and -11.649034295.


Subproblem 1
x + 5.4 = 11.649034295

Simplifying
x + 5.4 = 11.649034295

Reorder the terms:
5.4 + x = 11.649034295

Solving
5.4 + x = 11.649034295

Solving for variable 'x'.

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

Add '-5.4' to each side of the equation.
5.4 + -5.4 + x = 11.649034295 + -5.4

Combine like terms: 5.4 + -5.4 = 0.0
0.0 + x = 11.649034295 + -5.4
x = 11.649034295 + -5.4

Combine like terms: 11.649034295 + -5.4 = 6.249034295
x = 6.249034295

Simplifying
x = 6.249034295


Subproblem 2
x + 5.4 = -11.649034295

Simplifying
x + 5.4 = -11.649034295

Reorder the terms:
5.4 + x = -11.649034295

Solving
5.4 + x = -11.649034295

Solving for variable 'x'.

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

Add '-5.4' to each side of the equation.
5.4 + -5.4 + x = -11.649034295 + -5.4

Combine like terms: 5.4 + -5.4 = 0.0
0.0 + x = -11.649034295 + -5.4
x = -11.649034295 + -5.4

Combine like terms: -11.649034295 + -5.4 = -17.049034295
x = -17.049034295

Simplifying
x = -17.049034295


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.249034295, -17.049034295}

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