2x^2-4x-6=1

Solution for 2x^2-4x-6=1 equation:

Simplifying
2x2 + -4x + -6 = 1

Reorder the terms:
-6 + -4x + 2x2 = 1

Solving
-6 + -4x + 2x2 = 1

Solving for variable 'x'.

Reorder the terms:
-6 + -1 + -4x + 2x2 = 1 + -1

Combine like terms: -6 + -1 = -7
-7 + -4x + 2x2 = 1 + -1

Combine like terms: 1 + -1 = 0
-7 + -4x + 2x2 = 0

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

Divide each side by '2'.
-3.5 + -2x + x2 = 0

Move the constant term to the right:

Add '3.5' to each side of the equation.
-3.5 + -2x + 3.5 + x2 = 0 + 3.5

Reorder the terms:
-3.5 + 3.5 + -2x + x2 = 0 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + -2x + x2 = 0 + 3.5
-2x + x2 = 0 + 3.5

Combine like terms: 0 + 3.5 = 3.5
-2x + x2 = 3.5

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 = 3.5 + 1

Reorder the terms:
1 + -2x + x2 = 3.5 + 1

Combine like terms: 3.5 + 1 = 4.5
1 + -2x + x2 = 4.5

Factor a perfect square on the left side:
(x + -1)(x + -1) = 4.5

Calculate the square root of the right side: 2.121320344

Break this problem into two subproblems by setting 
(x + -1) equal to 2.121320344 and -2.121320344.

Subproblem 1
x + -1 = 2.121320344

Simplifying
x + -1 = 2.121320344

Reorder the terms:
-1 + x = 2.121320344

Solving
-1 + x = 2.121320344

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 = 2.121320344 + 1

Combine like terms: -1 + 1 = 0
0 + x = 2.121320344 + 1
x = 2.121320344 + 1

Combine like terms: 2.121320344 + 1 = 3.121320344
x = 3.121320344

Simplifying
x = 3.121320344

Subproblem 2
x + -1 = -2.121320344

Simplifying
x + -1 = -2.121320344

Reorder the terms:
-1 + x = -2.121320344

Solving
-1 + x = -2.121320344

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 = -2.121320344 + 1

Combine like terms: -1 + 1 = 0
0 + x = -2.121320344 + 1
x = -2.121320344 + 1

Combine like terms: -2.121320344 + 1 = -1.121320344
x = -1.121320344

Simplifying
x = -1.121320344

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.121320344, -1.121320344}