11x^2+22x-1200=0

Solution for 11x^2+22x-1200=0 equation:

Simplifying
11x2 + 22x + -1200 = 0

Reorder the terms:
-1200 + 22x + 11x2 = 0

Solving
-1200 + 22x + 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'.
-109.0909091 + 2x + x2 = 0

Move the constant term to the right:

Add '109.0909091' to each side of the equation.
-109.0909091 + 2x + 109.0909091 + x2 = 0 + 109.0909091

Reorder the terms:
-109.0909091 + 109.0909091 + 2x + x2 = 0 + 109.0909091

Combine like terms: -109.0909091 + 109.0909091 = 0.0000000
0.0000000 + 2x + x2 = 0 + 109.0909091
2x + x2 = 0 + 109.0909091

Combine like terms: 0 + 109.0909091 = 109.0909091
2x + x2 = 109.0909091

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 109.0909091 + 1

Reorder the terms:
1 + 2x + x2 = 109.0909091 + 1

Combine like terms: 109.0909091 + 1 = 110.0909091
1 + 2x + x2 = 110.0909091

Factor a perfect square on the left side:
(x + 1)(x + 1) = 110.0909091

Calculate the square root of the right side: 10.492421508

Break this problem into two subproblems by setting 
(x + 1) equal to 10.492421508 and -10.492421508.

Subproblem 1
x + 1 = 10.492421508

Simplifying
x + 1 = 10.492421508

Reorder the terms:
1 + x = 10.492421508

Solving
1 + x = 10.492421508

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = 10.492421508 + -1

Combine like terms: 1 + -1 = 0
0 + x = 10.492421508 + -1
x = 10.492421508 + -1

Combine like terms: 10.492421508 + -1 = 9.492421508
x = 9.492421508

Simplifying
x = 9.492421508

Subproblem 2
x + 1 = -10.492421508

Simplifying
x + 1 = -10.492421508

Reorder the terms:
1 + x = -10.492421508

Solving
1 + x = -10.492421508

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = -10.492421508 + -1

Combine like terms: 1 + -1 = 0
0 + x = -10.492421508 + -1
x = -10.492421508 + -1

Combine like terms: -10.492421508 + -1 = -11.492421508
x = -11.492421508

Simplifying
x = -11.492421508

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.492421508, -11.492421508}