1.1q^2-10q-100=0

Solution for 1.1q^2-10q-100=0 equation:

Simplifying
1.1q2 + -10q + -100 = 0

Reorder the terms:
-100 + -10q + 1.1q2 = 0

Solving
-100 + -10q + 1.1q2 = 0

Solving for variable 'q'.

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

Divide each side by '1.1'.
-90.90909091 + -9.090909091q + q2 = 0

Move the constant term to the right:

Add '90.90909091' to each side of the equation.
-90.90909091 + -9.090909091q + 90.90909091 + q2 = 0 + 90.90909091

Reorder the terms:
-90.90909091 + 90.90909091 + -9.090909091q + q2 = 0 + 90.90909091

Combine like terms: -90.90909091 + 90.90909091 = 0.00000000
0.00000000 + -9.090909091q + q2 = 0 + 90.90909091
-9.090909091q + q2 = 0 + 90.90909091

Combine like terms: 0 + 90.90909091 = 90.90909091
-9.090909091q + q2 = 90.90909091

The q term is -9.090909091q.  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.
-9.090909091q + 20.66115703 + q2 = 90.90909091 + 20.66115703

Reorder the terms:
20.66115703 + -9.090909091q + q2 = 90.90909091 + 20.66115703

Combine like terms: 90.90909091 + 20.66115703 = 111.57024794
20.66115703 + -9.090909091q + q2 = 111.57024794

Factor a perfect square on the left side:
(q + -4.545454546)(q + -4.545454546) = 111.57024794

Calculate the square root of the right side: 10.562681854

Break this problem into two subproblems by setting 
(q + -4.545454546) equal to 10.562681854 and -10.562681854.

Subproblem 1
q + -4.545454546 = 10.562681854

Simplifying
q + -4.545454546 = 10.562681854

Reorder the terms:
-4.545454546 + q = 10.562681854

Solving
-4.545454546 + q = 10.562681854

Solving for variable 'q'.

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

Add '4.545454546' to each side of the equation.
-4.545454546 + 4.545454546 + q = 10.562681854 + 4.545454546

Combine like terms: -4.545454546 + 4.545454546 = 0.000000000
0.000000000 + q = 10.562681854 + 4.545454546
q = 10.562681854 + 4.545454546

Combine like terms: 10.562681854 + 4.545454546 = 15.1081364
q = 15.1081364

Simplifying
q = 15.1081364

Subproblem 2
q + -4.545454546 = -10.562681854

Simplifying
q + -4.545454546 = -10.562681854

Reorder the terms:
-4.545454546 + q = -10.562681854

Solving
-4.545454546 + q = -10.562681854

Solving for variable 'q'.

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

Add '4.545454546' to each side of the equation.
-4.545454546 + 4.545454546 + q = -10.562681854 + 4.545454546

Combine like terms: -4.545454546 + 4.545454546 = 0.000000000
0.000000000 + q = -10.562681854 + 4.545454546
q = -10.562681854 + 4.545454546

Combine like terms: -10.562681854 + 4.545454546 = -6.017227308
q = -6.017227308

Simplifying
q = -6.017227308

Solution
The solution to the problem is based on the solutions
from the subproblems.
q = {15.1081364, -6.017227308}