10x^2-22x-6=0

Solution for 10x^2-22x-6=0 equation:

Simplifying
10x2 + -22x + -6 = 0

Reorder the terms:
-6 + -22x + 10x2 = 0

Solving
-6 + -22x + 10x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + -11x + 5x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + -11x + 5x2)' equal to zero and attempt to solve:

Simplifying
-3 + -11x + 5x2 = 0

Solving
-3 + -11x + 5x2 = 0

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

Divide each side by '5'.
-0.6 + -2.2x + x2 = 0

Move the constant term to the right:

Add '0.6' to each side of the equation.
-0.6 + -2.2x + 0.6 + x2 = 0 + 0.6

Reorder the terms:
-0.6 + 0.6 + -2.2x + x2 = 0 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + -2.2x + x2 = 0 + 0.6
-2.2x + x2 = 0 + 0.6

Combine like terms: 0 + 0.6 = 0.6
-2.2x + x2 = 0.6

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 = 0.6 + 1.21

Reorder the terms:
1.21 + -2.2x + x2 = 0.6 + 1.21

Combine like terms: 0.6 + 1.21 = 1.81
1.21 + -2.2x + x2 = 1.81

Factor a perfect square on the left side:
(x + -1.1)(x + -1.1) = 1.81

Calculate the square root of the right side: 1.345362405

Break this problem into two subproblems by setting 
(x + -1.1) equal to 1.345362405 and -1.345362405.

Subproblem 1
x + -1.1 = 1.345362405

Simplifying
x + -1.1 = 1.345362405

Reorder the terms:
-1.1 + x = 1.345362405

Solving
-1.1 + x = 1.345362405

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 = 1.345362405 + 1.1

Combine like terms: -1.1 + 1.1 = 0.0
0.0 + x = 1.345362405 + 1.1
x = 1.345362405 + 1.1

Combine like terms: 1.345362405 + 1.1 = 2.445362405
x = 2.445362405

Simplifying
x = 2.445362405

Subproblem 2
x + -1.1 = -1.345362405

Simplifying
x + -1.1 = -1.345362405

Reorder the terms:
-1.1 + x = -1.345362405

Solving
-1.1 + x = -1.345362405

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 = -1.345362405 + 1.1

Combine like terms: -1.1 + 1.1 = 0.0
0.0 + x = -1.345362405 + 1.1
x = -1.345362405 + 1.1

Combine like terms: -1.345362405 + 1.1 = -0.245362405
x = -0.245362405

Simplifying
x = -0.245362405

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.445362405, -0.245362405}
Solution
x = {2.445362405, -0.245362405}