5x^2-11x-1=0

Solution for 5x^2-11x-1=0 equation:

Simplifying
5x2 + -11x + -1 = 0

Reorder the terms:
-1 + -11x + 5x2 = 0

Solving
-1 + -11x + 5x2 = 0

Solving for variable 'x'.

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

Divide each side by '5'.
-0.2 + -2.2x + x2 = 0

Move the constant term to the right:

Add '0.2' to each side of the equation.
-0.2 + -2.2x + 0.2 + x2 = 0 + 0.2

Reorder the terms:
-0.2 + 0.2 + -2.2x + x2 = 0 + 0.2

Combine like terms: -0.2 + 0.2 = 0.0
0.0 + -2.2x + x2 = 0 + 0.2
-2.2x + x2 = 0 + 0.2

Combine like terms: 0 + 0.2 = 0.2
-2.2x + x2 = 0.2

The x term is -2.2x.  Take half its coefficient (-1.1).
Square it (1.21) and add it to both sides.

Add '1.21' to each side of the equation.
-2.2x + 1.21 + x2 = 0.2 + 1.21

Reorder the terms:
1.21 + -2.2x + x2 = 0.2 + 1.21

Combine like terms: 0.2 + 1.21 = 1.41
1.21 + -2.2x + x2 = 1.41

Factor a perfect square on the left side:
(x + -1.1)(x + -1.1) = 1.41

Calculate the square root of the right side: 1.187434209

Break this problem into two subproblems by setting 
(x + -1.1) equal to 1.187434209 and -1.187434209.

Subproblem 1
x + -1.1 = 1.187434209

Simplifying
x + -1.1 = 1.187434209

Reorder the terms:
-1.1 + x = 1.187434209

Solving
-1.1 + x = 1.187434209

Solving for variable 'x'.

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

Add '1.1' to each side of the equation.
-1.1 + 1.1 + x = 1.187434209 + 1.1

Combine like terms: -1.1 + 1.1 = 0.0
0.0 + x = 1.187434209 + 1.1
x = 1.187434209 + 1.1

Combine like terms: 1.187434209 + 1.1 = 2.287434209
x = 2.287434209

Simplifying
x = 2.287434209

Subproblem 2
x + -1.1 = -1.187434209

Simplifying
x + -1.1 = -1.187434209

Reorder the terms:
-1.1 + x = -1.187434209

Solving
-1.1 + x = -1.187434209

Solving for variable 'x'.

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

Add '1.1' to each side of the equation.
-1.1 + 1.1 + x = -1.187434209 + 1.1

Combine like terms: -1.1 + 1.1 = 0.0
0.0 + x = -1.187434209 + 1.1
x = -1.187434209 + 1.1

Combine like terms: -1.187434209 + 1.1 = -0.087434209
x = -0.087434209

Simplifying
x = -0.087434209

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.287434209, -0.087434209}