2x*(x-1)=7

Solution for 2x*(x-1)=7 equation:

Simplifying
2x(x + -1) = 7

Reorder the terms:
2x(-1 + x) = 7
(-1 * 2x + x * 2x) = 7
(-2x + 2x2) = 7

Solving
-2x + 2x2 = 7

Solving for variable 'x'.

Reorder the terms:
-7 + -2x + 2x2 = 7 + -7

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

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

Divide each side by '2'.
-3.5 + -1x + x2 = 0

Move the constant term to the right:

Add '3.5' to each side of the equation.
-3.5 + -1x + 3.5 + x2 = 0 + 3.5

Reorder the terms:
-3.5 + 3.5 + -1x + x2 = 0 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + -1x + x2 = 0 + 3.5
-1x + x2 = 0 + 3.5

Combine like terms: 0 + 3.5 = 3.5
-1x + x2 = 3.5

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = 3.5 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 3.5 + 0.25

Combine like terms: 3.5 + 0.25 = 3.75
0.25 + -1x + x2 = 3.75

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 3.75

Calculate the square root of the right side: 1.936491673

Break this problem into two subproblems by setting 
(x + -0.5) equal to 1.936491673 and -1.936491673.

Subproblem 1
x + -0.5 = 1.936491673

Simplifying
x + -0.5 = 1.936491673

Reorder the terms:
-0.5 + x = 1.936491673

Solving
-0.5 + x = 1.936491673

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = 1.936491673 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 1.936491673 + 0.5
x = 1.936491673 + 0.5

Combine like terms: 1.936491673 + 0.5 = 2.436491673
x = 2.436491673

Simplifying
x = 2.436491673

Subproblem 2
x + -0.5 = -1.936491673

Simplifying
x + -0.5 = -1.936491673

Reorder the terms:
-0.5 + x = -1.936491673

Solving
-0.5 + x = -1.936491673

Solving for variable 'x'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = -1.936491673 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -1.936491673 + 0.5
x = -1.936491673 + 0.5

Combine like terms: -1.936491673 + 0.5 = -1.436491673
x = -1.436491673

Simplifying
x = -1.436491673

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.436491673, -1.436491673}