10x^2-20x-6=0

Solution for 10x^2-20x-6=0 equation:

Simplifying
10x2 + -20x + -6 = 0

Reorder the terms:
-6 + -20x + 10x2 = 0

Solving
-6 + -20x + 10x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + -10x + 5x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + -10x + 5x2)' equal to zero and attempt to solve:

Simplifying
-3 + -10x + 5x2 = 0

Solving
-3 + -10x + 5x2 = 0

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

Divide each side by '5'.
-0.6 + -2x + x2 = 0

Move the constant term to the right:

Add '0.6' to each side of the equation.
-0.6 + -2x + 0.6 + x2 = 0 + 0.6

Reorder the terms:
-0.6 + 0.6 + -2x + x2 = 0 + 0.6

Combine like terms: -0.6 + 0.6 = 0.0
0.0 + -2x + x2 = 0 + 0.6
-2x + x2 = 0 + 0.6

Combine like terms: 0 + 0.6 = 0.6
-2x + x2 = 0.6

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 0.6 + 1

Reorder the terms:
1 + -2x + x2 = 0.6 + 1

Combine like terms: 0.6 + 1 = 1.6
1 + -2x + x2 = 1.6

Factor a perfect square on the left side:
(x + -1)(x + -1) = 1.6

Calculate the square root of the right side: 1.264911064

Break this problem into two subproblems by setting 
(x + -1) equal to 1.264911064 and -1.264911064.

Subproblem 1
x + -1 = 1.264911064

Simplifying
x + -1 = 1.264911064

Reorder the terms:
-1 + x = 1.264911064

Solving
-1 + x = 1.264911064

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = 1.264911064 + 1

Combine like terms: -1 + 1 = 0
0 + x = 1.264911064 + 1
x = 1.264911064 + 1

Combine like terms: 1.264911064 + 1 = 2.264911064
x = 2.264911064

Simplifying
x = 2.264911064

Subproblem 2
x + -1 = -1.264911064

Simplifying
x + -1 = -1.264911064

Reorder the terms:
-1 + x = -1.264911064

Solving
-1 + x = -1.264911064

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = -1.264911064 + 1

Combine like terms: -1 + 1 = 0
0 + x = -1.264911064 + 1
x = -1.264911064 + 1

Combine like terms: -1.264911064 + 1 = -0.264911064
x = -0.264911064

Simplifying
x = -0.264911064

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.264911064, -0.264911064}
Solution
x = {2.264911064, -0.264911064}