0.05x^2+1.1x-200=0

Solution for 0.05x^2+1.1x-200=0 equation:

Simplifying
0.05x2 + 1.1x + -200 = 0

Reorder the terms:
-200 + 1.1x + 0.05x2 = 0

Solving
-200 + 1.1x + 0.05x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.05'.
-4000 + 22x + x2 = 0

Move the constant term to the right:

Add '4000' to each side of the equation.
-4000 + 22x + 4000 + x2 = 0 + 4000

Reorder the terms:
-4000 + 4000 + 22x + x2 = 0 + 4000

Combine like terms: -4000 + 4000 = 0
0 + 22x + x2 = 0 + 4000
22x + x2 = 0 + 4000

Combine like terms: 0 + 4000 = 4000
22x + x2 = 4000

The x term is 22x.  Take half its coefficient (11).
Square it (121) and add it to both sides.

Add '121' to each side of the equation.
22x + 121 + x2 = 4000 + 121

Reorder the terms:
121 + 22x + x2 = 4000 + 121

Combine like terms: 4000 + 121 = 4121
121 + 22x + x2 = 4121

Factor a perfect square on the left side:
(x + 11)(x + 11) = 4121

Calculate the square root of the right side: 64.195015383

Break this problem into two subproblems by setting 
(x + 11) equal to 64.195015383 and -64.195015383.

Subproblem 1
x + 11 = 64.195015383

Simplifying
x + 11 = 64.195015383

Reorder the terms:
11 + x = 64.195015383

Solving
11 + x = 64.195015383

Solving for variable 'x'.

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

Add '-11' to each side of the equation.
11 + -11 + x = 64.195015383 + -11

Combine like terms: 11 + -11 = 0
0 + x = 64.195015383 + -11
x = 64.195015383 + -11

Combine like terms: 64.195015383 + -11 = 53.195015383
x = 53.195015383

Simplifying
x = 53.195015383

Subproblem 2
x + 11 = -64.195015383

Simplifying
x + 11 = -64.195015383

Reorder the terms:
11 + x = -64.195015383

Solving
11 + x = -64.195015383

Solving for variable 'x'.

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

Add '-11' to each side of the equation.
11 + -11 + x = -64.195015383 + -11

Combine like terms: 11 + -11 = 0
0 + x = -64.195015383 + -11
x = -64.195015383 + -11

Combine like terms: -64.195015383 + -11 = -75.195015383
x = -75.195015383

Simplifying
x = -75.195015383

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {53.195015383, -75.195015383}