0.25x^2-8x+64=0

Solution for 0.25x^2-8x+64=0 equation:

Simplifying
0.25x2 + -8x + 64 = 0

Reorder the terms:
64 + -8x + 0.25x2 = 0

Solving
64 + -8x + 0.25x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.25'.
256 + -32x + x2 = 0

Move the constant term to the right:

Add '-256' to each side of the equation.
256 + -32x + -256 + x2 = 0 + -256

Reorder the terms:
256 + -256 + -32x + x2 = 0 + -256

Combine like terms: 256 + -256 = 0
0 + -32x + x2 = 0 + -256
-32x + x2 = 0 + -256

Combine like terms: 0 + -256 = -256
-32x + x2 = -256

The x term is -32x.  Take half its coefficient (-16).
Square it (256) and add it to both sides.

Add '256' to each side of the equation.
-32x + 256 + x2 = -256 + 256

Reorder the terms:
256 + -32x + x2 = -256 + 256

Combine like terms: -256 + 256 = 0
256 + -32x + x2 = 0

Factor a perfect square on the left side:
(x + -16)(x + -16) = 0

Calculate the square root of the right side: 0

Break this problem into two subproblems by setting 
(x + -16) equal to 0 and 0.

Subproblem 1
x + -16 = 0

Simplifying
x + -16 = 0

Reorder the terms:
-16 + x = 0

Solving
-16 + x = 0

Solving for variable 'x'.

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

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

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

Combine like terms: 0 + 16 = 16
x = 16

Simplifying
x = 16

Subproblem 2
x + -16 = 0

Simplifying
x + -16 = 0

Reorder the terms:
-16 + x = 0

Solving
-16 + x = 0

Solving for variable 'x'.

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

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

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

Combine like terms: 0 + 16 = 16
x = 16

Simplifying
x = 16

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {16, 16}