53.3(.5-x)(.5-x)=(2x)(2x)

Solution for 53.3(.5-x)(.5-x)=(2x)(2x) equation:

Simplifying
53.3(0.5 + -1x)(0.5 + -1x) = (2x)(2x)

Multiply (0.5 + -1x) * (0.5 + -1x)
53.3(0.5(0.5 + -1x) + -1x * (0.5 + -1x)) = (2x)(2x)
53.3((0.5 * 0.5 + -1x * 0.5) + -1x * (0.5 + -1x)) = (2x)(2x)
53.3((0.25 + -0.5x) + -1x * (0.5 + -1x)) = (2x)(2x)
53.3(0.25 + -0.5x + (0.5 * -1x + -1x * -1x)) = (2x)(2x)
53.3(0.25 + -0.5x + (-0.5x + 1x2)) = (2x)(2x)

Combine like terms: -0.5x + -0.5x = -1x
53.3(0.25 + -1x + 1x2) = (2x)(2x)
(0.25 * 53.3 + -1x * 53.3 + 1x2 * 53.3) = (2x)(2x)
(13.325 + -53.3x + 53.3x2) = (2x)(2x)

Remove parenthesis around (2x)
13.325 + -53.3x + 53.3x2 = 2x(2x)

Remove parenthesis around (2x)
13.325 + -53.3x + 53.3x2 = 2x * 2x

Reorder the terms for easier multiplication:
13.325 + -53.3x + 53.3x2 = 2 * 2x * x

Multiply 2 * 2
13.325 + -53.3x + 53.3x2 = 4x * x

Multiply x * x
13.325 + -53.3x + 53.3x2 = 4x2

Solving
13.325 + -53.3x + 53.3x2 = 4x2

Solving for variable 'x'.

Combine like terms: 53.3x2 + -4x2 = 49.3x2
13.325 + -53.3x + 49.3x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
13.325 + -53.3x + 49.3x2 = 0

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

Divide each side by '49.3'.
0.2702839757 + -1.081135903x + x2 = 0

Move the constant term to the right:

Add '-0.2702839757' to each side of the equation.
0.2702839757 + -1.081135903x + -0.2702839757 + x2 = 0 + -0.2702839757

Reorder the terms:
0.2702839757 + -0.2702839757 + -1.081135903x + x2 = 0 + -0.2702839757

Combine like terms: 0.2702839757 + -0.2702839757 = 0.0000000000
0.0000000000 + -1.081135903x + x2 = 0 + -0.2702839757
-1.081135903x + x2 = 0 + -0.2702839757

Combine like terms: 0 + -0.2702839757 = -0.2702839757
-1.081135903x + x2 = -0.2702839757

The x term is -1.081135903x.  Take half its coefficient (-0.5405679515).
Square it (0.2922137102) and add it to both sides.

Add '0.2922137102' to each side of the equation.
-1.081135903x + 0.2922137102 + x2 = -0.2702839757 + 0.2922137102

Reorder the terms:
0.2922137102 + -1.081135903x + x2 = -0.2702839757 + 0.2922137102

Combine like terms: -0.2702839757 + 0.2922137102 = 0.0219297345
0.2922137102 + -1.081135903x + x2 = 0.0219297345

Factor a perfect square on the left side:
(x + -0.5405679515)(x + -0.5405679515) = 0.0219297345

Calculate the square root of the right side: 0.148086915

Break this problem into two subproblems by setting 
(x + -0.5405679515) equal to 0.148086915 and -0.148086915.

Subproblem 1
x + -0.5405679515 = 0.148086915

Simplifying
x + -0.5405679515 = 0.148086915

Reorder the terms:
-0.5405679515 + x = 0.148086915

Solving
-0.5405679515 + x = 0.148086915

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '0.5405679515' to each side of the equation.
-0.5405679515 + 0.5405679515 + x = 0.148086915 + 0.5405679515

Combine like terms: -0.5405679515 + 0.5405679515 = 0.0000000000
0.0000000000 + x = 0.148086915 + 0.5405679515
x = 0.148086915 + 0.5405679515

Combine like terms: 0.148086915 + 0.5405679515 = 0.6886548665
x = 0.6886548665

Simplifying
x = 0.6886548665

Subproblem 2
x + -0.5405679515 = -0.148086915

Simplifying
x + -0.5405679515 = -0.148086915

Reorder the terms:
-0.5405679515 + x = -0.148086915

Solving
-0.5405679515 + x = -0.148086915

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '0.5405679515' to each side of the equation.
-0.5405679515 + 0.5405679515 + x = -0.148086915 + 0.5405679515

Combine like terms: -0.5405679515 + 0.5405679515 = 0.0000000000
0.0000000000 + x = -0.148086915 + 0.5405679515
x = -0.148086915 + 0.5405679515

Combine like terms: -0.148086915 + 0.5405679515 = 0.3924810365
x = 0.3924810365

Simplifying
x = 0.3924810365

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.6886548665, 0.3924810365}