2x^2-48x+64=0

Solution for 2x^2-48x+64=0 equation:

Simplifying
2x2 + -48x + 64 = 0

Reorder the terms:
64 + -48x + 2x2 = 0

Solving
64 + -48x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(32 + -24x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(32 + -24x + x2)' equal to zero and attempt to solve:

Simplifying
32 + -24x + x2 = 0

Solving
32 + -24x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-32' to each side of the equation.
32 + -24x + -32 + x2 = 0 + -32

Reorder the terms:
32 + -32 + -24x + x2 = 0 + -32

Combine like terms: 32 + -32 = 0
0 + -24x + x2 = 0 + -32
-24x + x2 = 0 + -32

Combine like terms: 0 + -32 = -32
-24x + x2 = -32

The x term is -24x.  Take half its coefficient (-12).
Square it (144) and add it to both sides.

Add '144' to each side of the equation.
-24x + 144 + x2 = -32 + 144

Reorder the terms:
144 + -24x + x2 = -32 + 144

Combine like terms: -32 + 144 = 112
144 + -24x + x2 = 112

Factor a perfect square on the left side:
(x + -12)(x + -12) = 112

Calculate the square root of the right side: 10.583005244

Break this problem into two subproblems by setting 
(x + -12) equal to 10.583005244 and -10.583005244.

Subproblem 1
x + -12 = 10.583005244

Simplifying
x + -12 = 10.583005244

Reorder the terms:
-12 + x = 10.583005244

Solving
-12 + x = 10.583005244

Solving for variable 'x'.

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

Add '12' to each side of the equation.
-12 + 12 + x = 10.583005244 + 12

Combine like terms: -12 + 12 = 0
0 + x = 10.583005244 + 12
x = 10.583005244 + 12

Combine like terms: 10.583005244 + 12 = 22.583005244
x = 22.583005244

Simplifying
x = 22.583005244

Subproblem 2
x + -12 = -10.583005244

Simplifying
x + -12 = -10.583005244

Reorder the terms:
-12 + x = -10.583005244

Solving
-12 + x = -10.583005244

Solving for variable 'x'.

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

Add '12' to each side of the equation.
-12 + 12 + x = -10.583005244 + 12

Combine like terms: -12 + 12 = 0
0 + x = -10.583005244 + 12
x = -10.583005244 + 12

Combine like terms: -10.583005244 + 12 = 1.416994756
x = 1.416994756

Simplifying
x = 1.416994756

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {22.583005244, 1.416994756}
Solution
x = {22.583005244, 1.416994756}