2x(x-1)=91

Solution for 2x(x-1)=91 equation:

Simplifying
2x(x + -1) = 91

Reorder the terms:
2x(-1 + x) = 91
(-1 * 2x + x * 2x) = 91
(-2x + 2x2) = 91

Solving
-2x + 2x2 = 91

Solving for variable 'x'.

Reorder the terms:
-91 + -2x + 2x2 = 91 + -91

Combine like terms: 91 + -91 = 0
-91 + -2x + 2x2 = 0

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

Divide each side by '2'.
-45.5 + -1x + x2 = 0

Move the constant term to the right:

Add '45.5' to each side of the equation.
-45.5 + -1x + 45.5 + x2 = 0 + 45.5

Reorder the terms:
-45.5 + 45.5 + -1x + x2 = 0 + 45.5

Combine like terms: -45.5 + 45.5 = 0.0
0.0 + -1x + x2 = 0 + 45.5
-1x + x2 = 0 + 45.5

Combine like terms: 0 + 45.5 = 45.5
-1x + x2 = 45.5

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 = 45.5 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 45.5 + 0.25

Combine like terms: 45.5 + 0.25 = 45.75
0.25 + -1x + x2 = 45.75

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 45.75

Calculate the square root of the right side: 6.763874629

Break this problem into two subproblems by setting 
(x + -0.5) equal to 6.763874629 and -6.763874629.

Subproblem 1
x + -0.5 = 6.763874629

Simplifying
x + -0.5 = 6.763874629

Reorder the terms:
-0.5 + x = 6.763874629

Solving
-0.5 + x = 6.763874629

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 = 6.763874629 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 6.763874629 + 0.5
x = 6.763874629 + 0.5

Combine like terms: 6.763874629 + 0.5 = 7.263874629
x = 7.263874629

Simplifying
x = 7.263874629

Subproblem 2
x + -0.5 = -6.763874629

Simplifying
x + -0.5 = -6.763874629

Reorder the terms:
-0.5 + x = -6.763874629

Solving
-0.5 + x = -6.763874629

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 = -6.763874629 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -6.763874629 + 0.5
x = -6.763874629 + 0.5

Combine like terms: -6.763874629 + 0.5 = -6.263874629
x = -6.263874629

Simplifying
x = -6.263874629

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.263874629, -6.263874629}