x^2-48x+64=0

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

Simplifying
x2 + -48x + 64 = 0

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

Solving
64 + -48x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-64' to each side of the equation.
64 + -48x + -64 + x2 = 0 + -64

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

Combine like terms: 64 + -64 = 0
0 + -48x + x2 = 0 + -64
-48x + x2 = 0 + -64

Combine like terms: 0 + -64 = -64
-48x + x2 = -64

The x term is -48x.  Take half its coefficient (-24).
Square it (576) and add it to both sides.

Add '576' to each side of the equation.
-48x + 576 + x2 = -64 + 576

Reorder the terms:
576 + -48x + x2 = -64 + 576

Combine like terms: -64 + 576 = 512
576 + -48x + x2 = 512

Factor a perfect square on the left side:
(x + -24)(x + -24) = 512

Calculate the square root of the right side: 22.627416998

Break this problem into two subproblems by setting 
(x + -24) equal to 22.627416998 and -22.627416998.

Subproblem 1
x + -24 = 22.627416998

Simplifying
x + -24 = 22.627416998

Reorder the terms:
-24 + x = 22.627416998

Solving
-24 + x = 22.627416998

Solving for variable 'x'.

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

Add '24' to each side of the equation.
-24 + 24 + x = 22.627416998 + 24

Combine like terms: -24 + 24 = 0
0 + x = 22.627416998 + 24
x = 22.627416998 + 24

Combine like terms: 22.627416998 + 24 = 46.627416998
x = 46.627416998

Simplifying
x = 46.627416998

Subproblem 2
x + -24 = -22.627416998

Simplifying
x + -24 = -22.627416998

Reorder the terms:
-24 + x = -22.627416998

Solving
-24 + x = -22.627416998

Solving for variable 'x'.

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

Add '24' to each side of the equation.
-24 + 24 + x = -22.627416998 + 24

Combine like terms: -24 + 24 = 0
0 + x = -22.627416998 + 24
x = -22.627416998 + 24

Combine like terms: -22.627416998 + 24 = 1.372583002
x = 1.372583002

Simplifying
x = 1.372583002

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {46.627416998, 1.372583002}