2x(x-1)=16

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Solution for 2x(x-1)=16 equation: 


Simplifying
2x(x + -1) = 16

Reorder the terms:
2x(-1 + x) = 16
(-1 * 2x + x * 2x) = 16
(-2x + 2x2) = 16

Solving
-2x + 2x2 = 16

Solving for variable 'x'.

Reorder the terms:
-16 + -2x + 2x2 = 16 + -16

Combine like terms: 16 + -16 = 0
-16 + -2x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-8 + -1x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-8 + -1x + x2)' equal to zero and attempt to solve:

Simplifying
-8 + -1x + x2 = 0

Solving
-8 + -1x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + -1x + 8 + x2 = 0 + 8

Reorder the terms:
-8 + 8 + -1x + x2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1x + x2 = 0 + 8
-1x + x2 = 0 + 8

Combine like terms: 0 + 8 = 8
-1x + x2 = 8

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 = 8 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 8 + 0.25

Combine like terms: 8 + 0.25 = 8.25
0.25 + -1x + x2 = 8.25

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 8.25

Calculate the square root of the right side: 2.872281323

Break this problem into two subproblems by setting 
(x + -0.5) equal to 2.872281323 and -2.872281323.


Subproblem 1
x + -0.5 = 2.872281323

Simplifying
x + -0.5 = 2.872281323

Reorder the terms:
-0.5 + x = 2.872281323

Solving
-0.5 + x = 2.872281323

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 = 2.872281323 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 2.872281323 + 0.5
x = 2.872281323 + 0.5

Combine like terms: 2.872281323 + 0.5 = 3.372281323
x = 3.372281323

Simplifying
x = 3.372281323


Subproblem 2
x + -0.5 = -2.872281323

Simplifying
x + -0.5 = -2.872281323

Reorder the terms:
-0.5 + x = -2.872281323

Solving
-0.5 + x = -2.872281323

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 = -2.872281323 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -2.872281323 + 0.5
x = -2.872281323 + 0.5

Combine like terms: -2.872281323 + 0.5 = -2.372281323
x = -2.372281323

Simplifying
x = -2.372281323


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.372281323, -2.372281323}
Solution
x = {3.372281323, -2.372281323}

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