2x(x-2)=54

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Solution for 2x(x-2)=54 equation: 


Simplifying
2x(x + -2) = 54

Reorder the terms:
2x(-2 + x) = 54
(-2 * 2x + x * 2x) = 54
(-4x + 2x2) = 54

Solving
-4x + 2x2 = 54

Solving for variable 'x'.

Reorder the terms:
-54 + -4x + 2x2 = 54 + -54

Combine like terms: 54 + -54 = 0
-54 + -4x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-27 + -2x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-27 + -2x + x2)' equal to zero and attempt to solve:

Simplifying
-27 + -2x + x2 = 0

Solving
-27 + -2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '27' to each side of the equation.
-27 + -2x + 27 + x2 = 0 + 27

Reorder the terms:
-27 + 27 + -2x + x2 = 0 + 27

Combine like terms: -27 + 27 = 0
0 + -2x + x2 = 0 + 27
-2x + x2 = 0 + 27

Combine like terms: 0 + 27 = 27
-2x + x2 = 27

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 = 27 + 1

Reorder the terms:
1 + -2x + x2 = 27 + 1

Combine like terms: 27 + 1 = 28
1 + -2x + x2 = 28

Factor a perfect square on the left side:
(x + -1)(x + -1) = 28

Calculate the square root of the right side: 5.291502622

Break this problem into two subproblems by setting 
(x + -1) equal to 5.291502622 and -5.291502622.


Subproblem 1
x + -1 = 5.291502622

Simplifying
x + -1 = 5.291502622

Reorder the terms:
-1 + x = 5.291502622

Solving
-1 + x = 5.291502622

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 = 5.291502622 + 1

Combine like terms: -1 + 1 = 0
0 + x = 5.291502622 + 1
x = 5.291502622 + 1

Combine like terms: 5.291502622 + 1 = 6.291502622
x = 6.291502622

Simplifying
x = 6.291502622


Subproblem 2
x + -1 = -5.291502622

Simplifying
x + -1 = -5.291502622

Reorder the terms:
-1 + x = -5.291502622

Solving
-1 + x = -5.291502622

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 = -5.291502622 + 1

Combine like terms: -1 + 1 = 0
0 + x = -5.291502622 + 1
x = -5.291502622 + 1

Combine like terms: -5.291502622 + 1 = -4.291502622
x = -4.291502622

Simplifying
x = -4.291502622


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.291502622, -4.291502622}
Solution
x = {6.291502622, -4.291502622}

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