224=x(2x-4)

Solution for 224=x(2x-4) equation:

Simplifying
224 = x(2x + -4)

Reorder the terms:
224 = x(-4 + 2x)
224 = (-4 * x + 2x * x)
224 = (-4x + 2x2)

Solving
224 = -4x + 2x2

Solving for variable 'x'.

Reorder the terms:
224 + 4x + -2x2 = -4x + 4x + 2x2 + -2x2

Combine like terms: -4x + 4x = 0
224 + 4x + -2x2 = 0 + 2x2 + -2x2
224 + 4x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
224 + 4x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(112 + 2x + -1x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(112 + 2x + -1x2)' equal to zero and attempt to solve:

Simplifying
112 + 2x + -1x2 = 0

Solving
112 + 2x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-112 + -2x + x2 = 0

Move the constant term to the right:

Add '112' to each side of the equation.
-112 + -2x + 112 + x2 = 0 + 112

Reorder the terms:
-112 + 112 + -2x + x2 = 0 + 112

Combine like terms: -112 + 112 = 0
0 + -2x + x2 = 0 + 112
-2x + x2 = 0 + 112

Combine like terms: 0 + 112 = 112
-2x + x2 = 112

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 = 112 + 1

Reorder the terms:
1 + -2x + x2 = 112 + 1

Combine like terms: 112 + 1 = 113
1 + -2x + x2 = 113

Factor a perfect square on the left side:
(x + -1)(x + -1) = 113

Calculate the square root of the right side: 10.630145813

Break this problem into two subproblems by setting 
(x + -1) equal to 10.630145813 and -10.630145813.

Subproblem 1
x + -1 = 10.630145813

Simplifying
x + -1 = 10.630145813

Reorder the terms:
-1 + x = 10.630145813

Solving
-1 + x = 10.630145813

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 = 10.630145813 + 1

Combine like terms: -1 + 1 = 0
0 + x = 10.630145813 + 1
x = 10.630145813 + 1

Combine like terms: 10.630145813 + 1 = 11.630145813
x = 11.630145813

Simplifying
x = 11.630145813

Subproblem 2
x + -1 = -10.630145813

Simplifying
x + -1 = -10.630145813

Reorder the terms:
-1 + x = -10.630145813

Solving
-1 + x = -10.630145813

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 = -10.630145813 + 1

Combine like terms: -1 + 1 = 0
0 + x = -10.630145813 + 1
x = -10.630145813 + 1

Combine like terms: -10.630145813 + 1 = -9.630145813
x = -9.630145813

Simplifying
x = -9.630145813

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.630145813, -9.630145813}
Solution
x = {11.630145813, -9.630145813}