1.2x^2-100x-1.1=0

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Solution for 1.2x^2-100x-1.1=0 equation: 


Simplifying
1.2x2 + -100x + -1.1 = 0

Reorder the terms:
-1.1 + -100x + 1.2x2 = 0

Solving
-1.1 + -100x + 1.2x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
1.2 the coefficient of the squared term: 

Divide each side by '1.2'.
-0.9166666667 + -83.33333333x + x2 = 0

Move the constant term to the right:

Add '0.9166666667' to each side of the equation.
-0.9166666667 + -83.33333333x + 0.9166666667 + x2 = 0 + 0.9166666667

Reorder the terms:
-0.9166666667 + 0.9166666667 + -83.33333333x + x2 = 0 + 0.9166666667

Combine like terms: -0.9166666667 + 0.9166666667 = 0.0000000000
0.0000000000 + -83.33333333x + x2 = 0 + 0.9166666667
-83.33333333x + x2 = 0 + 0.9166666667

Combine like terms: 0 + 0.9166666667 = 0.9166666667
-83.33333333x + x2 = 0.9166666667

The x term is -83.33333333x.  Take half its coefficient (-41.66666667).
Square it (1736.111111) and add it to both sides.

Add '1736.111111' to each side of the equation.
-83.33333333x + 1736.111111 + x2 = 0.9166666667 + 1736.111111

Reorder the terms:
1736.111111 + -83.33333333x + x2 = 0.9166666667 + 1736.111111

Combine like terms: 0.9166666667 + 1736.111111 = 1737.0277776667
1736.111111 + -83.33333333x + x2 = 1737.0277776667

Factor a perfect square on the left side:
(x + -41.66666667)(x + -41.66666667) = 1737.0277776667

Calculate the square root of the right side: 41.677665214

Break this problem into two subproblems by setting 
(x + -41.66666667) equal to 41.677665214 and -41.677665214.


Subproblem 1
x + -41.66666667 = 41.677665214

Simplifying
x + -41.66666667 = 41.677665214

Reorder the terms:
-41.66666667 + x = 41.677665214

Solving
-41.66666667 + x = 41.677665214

Solving for variable 'x'.

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

Add '41.66666667' to each side of the equation.
-41.66666667 + 41.66666667 + x = 41.677665214 + 41.66666667

Combine like terms: -41.66666667 + 41.66666667 = 0.00000000
0.00000000 + x = 41.677665214 + 41.66666667
x = 41.677665214 + 41.66666667

Combine like terms: 41.677665214 + 41.66666667 = 83.344331884
x = 83.344331884

Simplifying
x = 83.344331884


Subproblem 2
x + -41.66666667 = -41.677665214

Simplifying
x + -41.66666667 = -41.677665214

Reorder the terms:
-41.66666667 + x = -41.677665214

Solving
-41.66666667 + x = -41.677665214

Solving for variable 'x'.

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

Add '41.66666667' to each side of the equation.
-41.66666667 + 41.66666667 + x = -41.677665214 + 41.66666667

Combine like terms: -41.66666667 + 41.66666667 = 0.00000000
0.00000000 + x = -41.677665214 + 41.66666667
x = -41.677665214 + 41.66666667

Combine like terms: -41.677665214 + 41.66666667 = -0.010998544
x = -0.010998544

Simplifying
x = -0.010998544


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {83.344331884, -0.010998544}

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