100-5x-x^2=11

Solution for 100-5x-x^2=11 equation:

Simplifying
100 + -5x + -1x2 = 11

Solving
100 + -5x + -1x2 = 11

Solving for variable 'x'.

Reorder the terms:
100 + -11 + -5x + -1x2 = 11 + -11

Combine like terms: 100 + -11 = 89
89 + -5x + -1x2 = 11 + -11

Combine like terms: 11 + -11 = 0
89 + -5x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-89 + 5x + x2 = 0

Move the constant term to the right:

Add '89' to each side of the equation.
-89 + 5x + 89 + x2 = 0 + 89

Reorder the terms:
-89 + 89 + 5x + x2 = 0 + 89

Combine like terms: -89 + 89 = 0
0 + 5x + x2 = 0 + 89
5x + x2 = 0 + 89

Combine like terms: 0 + 89 = 89
5x + x2 = 89

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 89 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 89 + 6.25

Combine like terms: 89 + 6.25 = 95.25
6.25 + 5x + x2 = 95.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 95.25

Calculate the square root of the right side: 9.759610648

Break this problem into two subproblems by setting 
(x + 2.5) equal to 9.759610648 and -9.759610648.

Subproblem 1
x + 2.5 = 9.759610648

Simplifying
x + 2.5 = 9.759610648

Reorder the terms:
2.5 + x = 9.759610648

Solving
2.5 + x = 9.759610648

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 9.759610648 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 9.759610648 + -2.5
x = 9.759610648 + -2.5

Combine like terms: 9.759610648 + -2.5 = 7.259610648
x = 7.259610648

Simplifying
x = 7.259610648

Subproblem 2
x + 2.5 = -9.759610648

Simplifying
x + 2.5 = -9.759610648

Reorder the terms:
2.5 + x = -9.759610648

Solving
2.5 + x = -9.759610648

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -9.759610648 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -9.759610648 + -2.5
x = -9.759610648 + -2.5

Combine like terms: -9.759610648 + -2.5 = -12.259610648
x = -12.259610648

Simplifying
x = -12.259610648

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.259610648, -12.259610648}