64(0.05-x)(0.08-x)=2x^2

Solution for 64(0.05-x)(0.08-x)=2x^2 equation:

Simplifying
64(0.05 + -1x)(0.08 + -1x) = 2x2

Multiply (0.05 + -1x) * (0.08 + -1x)
64(0.05(0.08 + -1x) + -1x * (0.08 + -1x)) = 2x2
64((0.08 * 0.05 + -1x * 0.05) + -1x * (0.08 + -1x)) = 2x2
64((0.004 + -0.05x) + -1x * (0.08 + -1x)) = 2x2
64(0.004 + -0.05x + (0.08 * -1x + -1x * -1x)) = 2x2
64(0.004 + -0.05x + (-0.08x + 1x2)) = 2x2

Combine like terms: -0.05x + -0.08x = -0.13x
64(0.004 + -0.13x + 1x2) = 2x2
(0.004 * 64 + -0.13x * 64 + 1x2 * 64) = 2x2
(0.256 + -8.32x + 64x2) = 2x2

Solving
0.256 + -8.32x + 64x2 = 2x2

Solving for variable 'x'.

Combine like terms: 64x2 + -2x2 = 62x2
0.256 + -8.32x + 62x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
0.256 + -8.32x + 62x2 = 0

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

Divide each side by '62'.
0.004129032258 + -0.1341935484x + x2 = 0

Move the constant term to the right:

Add '-0.004129032258' to each side of the equation.
0.004129032258 + -0.1341935484x + -0.004129032258 + x2 = 0 + -0.004129032258

Reorder the terms:
0.004129032258 + -0.004129032258 + -0.1341935484x + x2 = 0 + -0.004129032258

Combine like terms: 0.004129032258 + -0.004129032258 = 0.000000000000
0.000000000000 + -0.1341935484x + x2 = 0 + -0.004129032258
-0.1341935484x + x2 = 0 + -0.004129032258

Combine like terms: 0 + -0.004129032258 = -0.004129032258
-0.1341935484x + x2 = -0.004129032258

The x term is -0.1341935484x.  Take half its coefficient (-0.0670967742).
Square it (0.004501977108) and add it to both sides.

Add '0.004501977108' to each side of the equation.
-0.1341935484x + 0.004501977108 + x2 = -0.004129032258 + 0.004501977108

Reorder the terms:
0.004501977108 + -0.1341935484x + x2 = -0.004129032258 + 0.004501977108

Combine like terms: -0.004129032258 + 0.004501977108 = 0.00037294485
0.004501977108 + -0.1341935484x + x2 = 0.00037294485

Factor a perfect square on the left side:
(x + -0.0670967742)(x + -0.0670967742) = 0.00037294485

Calculate the square root of the right side: 0.01931178

Break this problem into two subproblems by setting 
(x + -0.0670967742) equal to 0.01931178 and -0.01931178.

Subproblem 1
x + -0.0670967742 = 0.01931178

Simplifying
x + -0.0670967742 = 0.01931178

Reorder the terms:
-0.0670967742 + x = 0.01931178

Solving
-0.0670967742 + x = 0.01931178

Solving for variable 'x'.

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

Add '0.0670967742' to each side of the equation.
-0.0670967742 + 0.0670967742 + x = 0.01931178 + 0.0670967742

Combine like terms: -0.0670967742 + 0.0670967742 = 0.0000000000
0.0000000000 + x = 0.01931178 + 0.0670967742
x = 0.01931178 + 0.0670967742

Combine like terms: 0.01931178 + 0.0670967742 = 0.0864085542
x = 0.0864085542

Simplifying
x = 0.0864085542

Subproblem 2
x + -0.0670967742 = -0.01931178

Simplifying
x + -0.0670967742 = -0.01931178

Reorder the terms:
-0.0670967742 + x = -0.01931178

Solving
-0.0670967742 + x = -0.01931178

Solving for variable 'x'.

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

Add '0.0670967742' to each side of the equation.
-0.0670967742 + 0.0670967742 + x = -0.01931178 + 0.0670967742

Combine like terms: -0.0670967742 + 0.0670967742 = 0.0000000000
0.0000000000 + x = -0.01931178 + 0.0670967742
x = -0.01931178 + 0.0670967742

Combine like terms: -0.01931178 + 0.0670967742 = 0.0477849942
x = 0.0477849942

Simplifying
x = 0.0477849942

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.0864085542, 0.0477849942}