2x(x-1)=66

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Solution for 2x(x-1)=66 equation: 


Simplifying
2x(x + -1) = 66

Reorder the terms:
2x(-1 + x) = 66
(-1 * 2x + x * 2x) = 66
(-2x + 2x2) = 66

Solving
-2x + 2x2 = 66

Solving for variable 'x'.

Reorder the terms:
-66 + -2x + 2x2 = 66 + -66

Combine like terms: 66 + -66 = 0
-66 + -2x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-33 + -1x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-33 + -1x + x2)' equal to zero and attempt to solve:

Simplifying
-33 + -1x + x2 = 0

Solving
-33 + -1x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '33' to each side of the equation.
-33 + -1x + 33 + x2 = 0 + 33

Reorder the terms:
-33 + 33 + -1x + x2 = 0 + 33

Combine like terms: -33 + 33 = 0
0 + -1x + x2 = 0 + 33
-1x + x2 = 0 + 33

Combine like terms: 0 + 33 = 33
-1x + x2 = 33

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 = 33 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 33 + 0.25

Combine like terms: 33 + 0.25 = 33.25
0.25 + -1x + x2 = 33.25

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 33.25

Calculate the square root of the right side: 5.766281297

Break this problem into two subproblems by setting 
(x + -0.5) equal to 5.766281297 and -5.766281297.


Subproblem 1
x + -0.5 = 5.766281297

Simplifying
x + -0.5 = 5.766281297

Reorder the terms:
-0.5 + x = 5.766281297

Solving
-0.5 + x = 5.766281297

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 = 5.766281297 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 5.766281297 + 0.5
x = 5.766281297 + 0.5

Combine like terms: 5.766281297 + 0.5 = 6.266281297
x = 6.266281297

Simplifying
x = 6.266281297


Subproblem 2
x + -0.5 = -5.766281297

Simplifying
x + -0.5 = -5.766281297

Reorder the terms:
-0.5 + x = -5.766281297

Solving
-0.5 + x = -5.766281297

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 = -5.766281297 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -5.766281297 + 0.5
x = -5.766281297 + 0.5

Combine like terms: -5.766281297 + 0.5 = -5.266281297
x = -5.266281297

Simplifying
x = -5.266281297


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.266281297, -5.266281297}
Solution
x = {6.266281297, -5.266281297}

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