11x^2-5x-5=0

Solution for 11x^2-5x-5=0 equation:

Simplifying
11x2 + -5x + -5 = 0

Reorder the terms:
-5 + -5x + 11x2 = 0

Solving
-5 + -5x + 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'.
-0.4545454545 + -0.4545454545x + x2 = 0

Move the constant term to the right:

Add '0.4545454545' to each side of the equation.
-0.4545454545 + -0.4545454545x + 0.4545454545 + x2 = 0 + 0.4545454545

Reorder the terms:
-0.4545454545 + 0.4545454545 + -0.4545454545x + x2 = 0 + 0.4545454545

Combine like terms: -0.4545454545 + 0.4545454545 = 0.0000000000
0.0000000000 + -0.4545454545x + x2 = 0 + 0.4545454545
-0.4545454545x + x2 = 0 + 0.4545454545

Combine like terms: 0 + 0.4545454545 = 0.4545454545
-0.4545454545x + x2 = 0.4545454545

The x term is -0.4545454545x.  Take half its coefficient (-0.2272727273).
Square it (0.05165289257) and add it to both sides.

Add '0.05165289257' to each side of the equation.
-0.4545454545x + 0.05165289257 + x2 = 0.4545454545 + 0.05165289257

Reorder the terms:
0.05165289257 + -0.4545454545x + x2 = 0.4545454545 + 0.05165289257

Combine like terms: 0.4545454545 + 0.05165289257 = 0.50619834707
0.05165289257 + -0.4545454545x + x2 = 0.50619834707

Factor a perfect square on the left side:
(x + -0.2272727273)(x + -0.2272727273) = 0.50619834707

Calculate the square root of the right side: 0.711476175

Break this problem into two subproblems by setting 
(x + -0.2272727273) equal to 0.711476175 and -0.711476175.

Subproblem 1
x + -0.2272727273 = 0.711476175

Simplifying
x + -0.2272727273 = 0.711476175

Reorder the terms:
-0.2272727273 + x = 0.711476175

Solving
-0.2272727273 + x = 0.711476175

Solving for variable 'x'.

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

Add '0.2272727273' to each side of the equation.
-0.2272727273 + 0.2272727273 + x = 0.711476175 + 0.2272727273

Combine like terms: -0.2272727273 + 0.2272727273 = 0.0000000000
0.0000000000 + x = 0.711476175 + 0.2272727273
x = 0.711476175 + 0.2272727273

Combine like terms: 0.711476175 + 0.2272727273 = 0.9387489023
x = 0.9387489023

Simplifying
x = 0.9387489023

Subproblem 2
x + -0.2272727273 = -0.711476175

Simplifying
x + -0.2272727273 = -0.711476175

Reorder the terms:
-0.2272727273 + x = -0.711476175

Solving
-0.2272727273 + x = -0.711476175

Solving for variable 'x'.

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

Add '0.2272727273' to each side of the equation.
-0.2272727273 + 0.2272727273 + x = -0.711476175 + 0.2272727273

Combine like terms: -0.2272727273 + 0.2272727273 = 0.0000000000
0.0000000000 + x = -0.711476175 + 0.2272727273
x = -0.711476175 + 0.2272727273

Combine like terms: -0.711476175 + 0.2272727273 = -0.4842034477
x = -0.4842034477

Simplifying
x = -0.4842034477

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.9387489023, -0.4842034477}