4x^2-48x+64=0

Solution for 4x^2-48x+64=0 equation:

Simplifying
4x2 + -48x + 64 = 0

Reorder the terms:
64 + -48x + 4x2 = 0

Solving
64 + -48x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(16 + -12x + x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(16 + -12x + x2)' equal to zero and attempt to solve:

Simplifying
16 + -12x + x2 = 0

Solving
16 + -12x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-16' to each side of the equation.
16 + -12x + -16 + x2 = 0 + -16

Reorder the terms:
16 + -16 + -12x + x2 = 0 + -16

Combine like terms: 16 + -16 = 0
0 + -12x + x2 = 0 + -16
-12x + x2 = 0 + -16

Combine like terms: 0 + -16 = -16
-12x + x2 = -16

The x term is -12x.  Take half its coefficient (-6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
-12x + 36 + x2 = -16 + 36

Reorder the terms:
36 + -12x + x2 = -16 + 36

Combine like terms: -16 + 36 = 20
36 + -12x + x2 = 20

Factor a perfect square on the left side:
(x + -6)(x + -6) = 20

Calculate the square root of the right side: 4.472135955

Break this problem into two subproblems by setting 
(x + -6) equal to 4.472135955 and -4.472135955.

Subproblem 1
x + -6 = 4.472135955

Simplifying
x + -6 = 4.472135955

Reorder the terms:
-6 + x = 4.472135955

Solving
-6 + x = 4.472135955

Solving for variable 'x'.

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

Add '6' to each side of the equation.
-6 + 6 + x = 4.472135955 + 6

Combine like terms: -6 + 6 = 0
0 + x = 4.472135955 + 6
x = 4.472135955 + 6

Combine like terms: 4.472135955 + 6 = 10.472135955
x = 10.472135955

Simplifying
x = 10.472135955

Subproblem 2
x + -6 = -4.472135955

Simplifying
x + -6 = -4.472135955

Reorder the terms:
-6 + x = -4.472135955

Solving
-6 + x = -4.472135955

Solving for variable 'x'.

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

Add '6' to each side of the equation.
-6 + 6 + x = -4.472135955 + 6

Combine like terms: -6 + 6 = 0
0 + x = -4.472135955 + 6
x = -4.472135955 + 6

Combine like terms: -4.472135955 + 6 = 1.527864045
x = 1.527864045

Simplifying
x = 1.527864045

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {10.472135955, 1.527864045}
Solution
x = {10.472135955, 1.527864045}