(-11x^2+133x+1200)+(-7x^2+95x+1100)=0

Solution for (-11x^2+133x+1200)+(-7x^2+95x+1100)=0 equation:

Simplifying
(-11x2 + 133x + 1200) + (-7x2 + 95x + 1100) = 0

Reorder the terms:
(1200 + 133x + -11x2) + (-7x2 + 95x + 1100) = 0

Remove parenthesis around (1200 + 133x + -11x2)
1200 + 133x + -11x2 + (-7x2 + 95x + 1100) = 0

Reorder the terms:
1200 + 133x + -11x2 + (1100 + 95x + -7x2) = 0

Remove parenthesis around (1100 + 95x + -7x2)
1200 + 133x + -11x2 + 1100 + 95x + -7x2 = 0

Reorder the terms:
1200 + 1100 + 133x + 95x + -11x2 + -7x2 = 0

Combine like terms: 1200 + 1100 = 2300
2300 + 133x + 95x + -11x2 + -7x2 = 0

Combine like terms: 133x + 95x = 228x
2300 + 228x + -11x2 + -7x2 = 0

Combine like terms: -11x2 + -7x2 = -18x2
2300 + 228x + -18x2 = 0

Solving
2300 + 228x + -18x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(1150 + 114x + -9x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(1150 + 114x + -9x2)' equal to zero and attempt to solve:

Simplifying
1150 + 114x + -9x2 = 0

Solving
1150 + 114x + -9x2 = 0

Begin completing the square.  Divide all terms by
-9 the coefficient of the squared term: 

Divide each side by '-9'.
-127.7777778 + -12.66666667x + x2 = 0

Move the constant term to the right:

Add '127.7777778' to each side of the equation.
-127.7777778 + -12.66666667x + 127.7777778 + x2 = 0 + 127.7777778

Reorder the terms:
-127.7777778 + 127.7777778 + -12.66666667x + x2 = 0 + 127.7777778

Combine like terms: -127.7777778 + 127.7777778 = 0.0000000
0.0000000 + -12.66666667x + x2 = 0 + 127.7777778
-12.66666667x + x2 = 0 + 127.7777778

Combine like terms: 0 + 127.7777778 = 127.7777778
-12.66666667x + x2 = 127.7777778

The x term is -12.66666667x.  Take half its coefficient (-6.333333335).
Square it (40.11111113) and add it to both sides.

Add '40.11111113' to each side of the equation.
-12.66666667x + 40.11111113 + x2 = 127.7777778 + 40.11111113

Reorder the terms:
40.11111113 + -12.66666667x + x2 = 127.7777778 + 40.11111113

Combine like terms: 127.7777778 + 40.11111113 = 167.88888893
40.11111113 + -12.66666667x + x2 = 167.88888893

Factor a perfect square on the left side:
(x + -6.333333335)(x + -6.333333335) = 167.88888893

Calculate the square root of the right side: 12.957194485

Break this problem into two subproblems by setting 
(x + -6.333333335) equal to 12.957194485 and -12.957194485.

Subproblem 1
x + -6.333333335 = 12.957194485

Simplifying
x + -6.333333335 = 12.957194485

Reorder the terms:
-6.333333335 + x = 12.957194485

Solving
-6.333333335 + x = 12.957194485

Solving for variable 'x'.

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

Add '6.333333335' to each side of the equation.
-6.333333335 + 6.333333335 + x = 12.957194485 + 6.333333335

Combine like terms: -6.333333335 + 6.333333335 = 0.000000000
0.000000000 + x = 12.957194485 + 6.333333335
x = 12.957194485 + 6.333333335

Combine like terms: 12.957194485 + 6.333333335 = 19.29052782
x = 19.29052782

Simplifying
x = 19.29052782

Subproblem 2
x + -6.333333335 = -12.957194485

Simplifying
x + -6.333333335 = -12.957194485

Reorder the terms:
-6.333333335 + x = -12.957194485

Solving
-6.333333335 + x = -12.957194485

Solving for variable 'x'.

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

Add '6.333333335' to each side of the equation.
-6.333333335 + 6.333333335 + x = -12.957194485 + 6.333333335

Combine like terms: -6.333333335 + 6.333333335 = 0.000000000
0.000000000 + x = -12.957194485 + 6.333333335
x = -12.957194485 + 6.333333335

Combine like terms: -12.957194485 + 6.333333335 = -6.62386115
x = -6.62386115

Simplifying
x = -6.62386115

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {19.29052782, -6.62386115}
Solution
x = {19.29052782, -6.62386115}