11x^2-100x-11=0

Solution for 11x^2-100x-11=0 equation:

Simplifying
11x2 + -100x + -11 = 0

Reorder the terms:
-11 + -100x + 11x2 = 0

Solving
-11 + -100x + 11x2 = 0

Solving for variable 'x'.

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

Divide each side by '11'.
-1 + -9.090909091x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -9.090909091x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + -9.090909091x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -9.090909091x + x2 = 0 + 1
-9.090909091x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
-9.090909091x + x2 = 1

The x term is -9.090909091x.  Take half its coefficient (-4.545454546).
Square it (20.66115703) and add it to both sides.

Add '20.66115703' to each side of the equation.
-9.090909091x + 20.66115703 + x2 = 1 + 20.66115703

Reorder the terms:
20.66115703 + -9.090909091x + x2 = 1 + 20.66115703

Combine like terms: 1 + 20.66115703 = 21.66115703
20.66115703 + -9.090909091x + x2 = 21.66115703

Factor a perfect square on the left side:
(x + -4.545454546)(x + -4.545454546) = 21.66115703

Calculate the square root of the right side: 4.654154814

Break this problem into two subproblems by setting 
(x + -4.545454546) equal to 4.654154814 and -4.654154814.

Subproblem 1
x + -4.545454546 = 4.654154814

Simplifying
x + -4.545454546 = 4.654154814

Reorder the terms:
-4.545454546 + x = 4.654154814

Solving
-4.545454546 + x = 4.654154814

Solving for variable 'x'.

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

Add '4.545454546' to each side of the equation.
-4.545454546 + 4.545454546 + x = 4.654154814 + 4.545454546

Combine like terms: -4.545454546 + 4.545454546 = 0.000000000
0.000000000 + x = 4.654154814 + 4.545454546
x = 4.654154814 + 4.545454546

Combine like terms: 4.654154814 + 4.545454546 = 9.19960936
x = 9.19960936

Simplifying
x = 9.19960936

Subproblem 2
x + -4.545454546 = -4.654154814

Simplifying
x + -4.545454546 = -4.654154814

Reorder the terms:
-4.545454546 + x = -4.654154814

Solving
-4.545454546 + x = -4.654154814

Solving for variable 'x'.

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

Add '4.545454546' to each side of the equation.
-4.545454546 + 4.545454546 + x = -4.654154814 + 4.545454546

Combine like terms: -4.545454546 + 4.545454546 = 0.000000000
0.000000000 + x = -4.654154814 + 4.545454546
x = -4.654154814 + 4.545454546

Combine like terms: -4.654154814 + 4.545454546 = -0.108700268
x = -0.108700268

Simplifying
x = -0.108700268

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.19960936, -0.108700268}