x^2+10.8x-196.89=0

Solution for x^2+10.8x-196.89=0 equation:

Simplifying
x2 + 10.8x + -196.89 = 0

Reorder the terms:
-196.89 + 10.8x + x2 = 0

Solving
-196.89 + 10.8x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '196.89' to each side of the equation.
-196.89 + 10.8x + 196.89 + x2 = 0 + 196.89

Reorder the terms:
-196.89 + 196.89 + 10.8x + x2 = 0 + 196.89

Combine like terms: -196.89 + 196.89 = 0.00
0.00 + 10.8x + x2 = 0 + 196.89
10.8x + x2 = 0 + 196.89

Combine like terms: 0 + 196.89 = 196.89
10.8x + x2 = 196.89

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 = 196.89 + 29.16

Reorder the terms:
29.16 + 10.8x + x2 = 196.89 + 29.16

Combine like terms: 196.89 + 29.16 = 226.05
29.16 + 10.8x + x2 = 226.05

Factor a perfect square on the left side:
(x + 5.4)(x + 5.4) = 226.05

Calculate the square root of the right side: 15.034959262

Break this problem into two subproblems by setting 
(x + 5.4) equal to 15.034959262 and -15.034959262.

Subproblem 1
x + 5.4 = 15.034959262

Simplifying
x + 5.4 = 15.034959262

Reorder the terms:
5.4 + x = 15.034959262

Solving
5.4 + x = 15.034959262

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 = 15.034959262 + -5.4

Combine like terms: 5.4 + -5.4 = 0.0
0.0 + x = 15.034959262 + -5.4
x = 15.034959262 + -5.4

Combine like terms: 15.034959262 + -5.4 = 9.634959262
x = 9.634959262

Simplifying
x = 9.634959262

Subproblem 2
x + 5.4 = -15.034959262

Simplifying
x + 5.4 = -15.034959262

Reorder the terms:
5.4 + x = -15.034959262

Solving
5.4 + x = -15.034959262

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 = -15.034959262 + -5.4

Combine like terms: 5.4 + -5.4 = 0.0
0.0 + x = -15.034959262 + -5.4
x = -15.034959262 + -5.4

Combine like terms: -15.034959262 + -5.4 = -20.434959262
x = -20.434959262

Simplifying
x = -20.434959262

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.634959262, -20.434959262}