(x^2-48x+72)=0

Solution for (x^2-48x+72)=0 equation:

Simplifying
(x2 + -48x + 72) = 0

Reorder the terms:
(72 + -48x + x2) = 0

Remove parenthesis around (72 + -48x + x2)
72 + -48x + x2 = 0

Solving
72 + -48x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-72' to each side of the equation.
72 + -48x + -72 + x2 = 0 + -72

Reorder the terms:
72 + -72 + -48x + x2 = 0 + -72

Combine like terms: 72 + -72 = 0
0 + -48x + x2 = 0 + -72
-48x + x2 = 0 + -72

Combine like terms: 0 + -72 = -72
-48x + x2 = -72

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 = -72 + 576

Reorder the terms:
576 + -48x + x2 = -72 + 576

Combine like terms: -72 + 576 = 504
576 + -48x + x2 = 504

Factor a perfect square on the left side:
(x + -24)(x + -24) = 504

Calculate the square root of the right side: 22.449944321

Break this problem into two subproblems by setting 
(x + -24) equal to 22.449944321 and -22.449944321.

Subproblem 1
x + -24 = 22.449944321

Simplifying
x + -24 = 22.449944321

Reorder the terms:
-24 + x = 22.449944321

Solving
-24 + x = 22.449944321

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 = 22.449944321 + 24

Combine like terms: -24 + 24 = 0
0 + x = 22.449944321 + 24
x = 22.449944321 + 24

Combine like terms: 22.449944321 + 24 = 46.449944321
x = 46.449944321

Simplifying
x = 46.449944321

Subproblem 2
x + -24 = -22.449944321

Simplifying
x + -24 = -22.449944321

Reorder the terms:
-24 + x = -22.449944321

Solving
-24 + x = -22.449944321

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 = -22.449944321 + 24

Combine like terms: -24 + 24 = 0
0 + x = -22.449944321 + 24
x = -22.449944321 + 24

Combine like terms: -22.449944321 + 24 = 1.550055679
x = 1.550055679

Simplifying
x = 1.550055679

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {46.449944321, 1.550055679}