1.1x^2-8x-200=6x+4

Solution for 1.1x^2-8x-200=6x+4 equation:

Simplifying
1.1x2 + -8x + -200 = 6x + 4

Reorder the terms:
-200 + -8x + 1.1x2 = 6x + 4

Reorder the terms:
-200 + -8x + 1.1x2 = 4 + 6x

Solving
-200 + -8x + 1.1x2 = 4 + 6x

Solving for variable 'x'.

Reorder the terms:
-200 + -4 + -8x + -6x + 1.1x2 = 4 + 6x + -4 + -6x

Combine like terms: -200 + -4 = -204
-204 + -8x + -6x + 1.1x2 = 4 + 6x + -4 + -6x

Combine like terms: -8x + -6x = -14x
-204 + -14x + 1.1x2 = 4 + 6x + -4 + -6x

Reorder the terms:
-204 + -14x + 1.1x2 = 4 + -4 + 6x + -6x

Combine like terms: 4 + -4 = 0
-204 + -14x + 1.1x2 = 0 + 6x + -6x
-204 + -14x + 1.1x2 = 6x + -6x

Combine like terms: 6x + -6x = 0
-204 + -14x + 1.1x2 = 0

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

Divide each side by '1.1'.
-185.4545455 + -12.72727273x + x2 = 0

Move the constant term to the right:

Add '185.4545455' to each side of the equation.
-185.4545455 + -12.72727273x + 185.4545455 + x2 = 0 + 185.4545455

Reorder the terms:
-185.4545455 + 185.4545455 + -12.72727273x + x2 = 0 + 185.4545455

Combine like terms: -185.4545455 + 185.4545455 = 0.0000000
0.0000000 + -12.72727273x + x2 = 0 + 185.4545455
-12.72727273x + x2 = 0 + 185.4545455

Combine like terms: 0 + 185.4545455 = 185.4545455
-12.72727273x + x2 = 185.4545455

The x term is -12.72727273x.  Take half its coefficient (-6.363636365).
Square it (40.49586779) and add it to both sides.

Add '40.49586779' to each side of the equation.
-12.72727273x + 40.49586779 + x2 = 185.4545455 + 40.49586779

Reorder the terms:
40.49586779 + -12.72727273x + x2 = 185.4545455 + 40.49586779

Combine like terms: 185.4545455 + 40.49586779 = 225.95041329
40.49586779 + -12.72727273x + x2 = 225.95041329

Factor a perfect square on the left side:
(x + -6.363636365)(x + -6.363636365) = 225.95041329

Calculate the square root of the right side: 15.031647058

Break this problem into two subproblems by setting 
(x + -6.363636365) equal to 15.031647058 and -15.031647058.

Subproblem 1
x + -6.363636365 = 15.031647058

Simplifying
x + -6.363636365 = 15.031647058

Reorder the terms:
-6.363636365 + x = 15.031647058

Solving
-6.363636365 + x = 15.031647058

Solving for variable 'x'.

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

Add '6.363636365' to each side of the equation.
-6.363636365 + 6.363636365 + x = 15.031647058 + 6.363636365

Combine like terms: -6.363636365 + 6.363636365 = 0.000000000
0.000000000 + x = 15.031647058 + 6.363636365
x = 15.031647058 + 6.363636365

Combine like terms: 15.031647058 + 6.363636365 = 21.395283423
x = 21.395283423

Simplifying
x = 21.395283423

Subproblem 2
x + -6.363636365 = -15.031647058

Simplifying
x + -6.363636365 = -15.031647058

Reorder the terms:
-6.363636365 + x = -15.031647058

Solving
-6.363636365 + x = -15.031647058

Solving for variable 'x'.

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

Add '6.363636365' to each side of the equation.
-6.363636365 + 6.363636365 + x = -15.031647058 + 6.363636365

Combine like terms: -6.363636365 + 6.363636365 = 0.000000000
0.000000000 + x = -15.031647058 + 6.363636365
x = -15.031647058 + 6.363636365

Combine like terms: -15.031647058 + 6.363636365 = -8.668010693
x = -8.668010693

Simplifying
x = -8.668010693

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {21.395283423, -8.668010693}