h^2-48h+48=0

Solution for h^2-48h+48=0 equation:

Simplifying
h2 + -48h + 48 = 0

Reorder the terms:
48 + -48h + h2 = 0

Solving
48 + -48h + h2 = 0

Solving for variable 'h'.

Begin completing the square.

Move the constant term to the right:

Add '-48' to each side of the equation.
48 + -48h + -48 + h2 = 0 + -48

Reorder the terms:
48 + -48 + -48h + h2 = 0 + -48

Combine like terms: 48 + -48 = 0
0 + -48h + h2 = 0 + -48
-48h + h2 = 0 + -48

Combine like terms: 0 + -48 = -48
-48h + h2 = -48

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

Add '576' to each side of the equation.
-48h + 576 + h2 = -48 + 576

Reorder the terms:
576 + -48h + h2 = -48 + 576

Combine like terms: -48 + 576 = 528
576 + -48h + h2 = 528

Factor a perfect square on the left side:
(h + -24)(h + -24) = 528

Calculate the square root of the right side: 22.978250586

Break this problem into two subproblems by setting 
(h + -24) equal to 22.978250586 and -22.978250586.

Subproblem 1
h + -24 = 22.978250586

Simplifying
h + -24 = 22.978250586

Reorder the terms:
-24 + h = 22.978250586

Solving
-24 + h = 22.978250586

Solving for variable 'h'.

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

Add '24' to each side of the equation.
-24 + 24 + h = 22.978250586 + 24

Combine like terms: -24 + 24 = 0
0 + h = 22.978250586 + 24
h = 22.978250586 + 24

Combine like terms: 22.978250586 + 24 = 46.978250586
h = 46.978250586

Simplifying
h = 46.978250586

Subproblem 2
h + -24 = -22.978250586

Simplifying
h + -24 = -22.978250586

Reorder the terms:
-24 + h = -22.978250586

Solving
-24 + h = -22.978250586

Solving for variable 'h'.

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

Add '24' to each side of the equation.
-24 + 24 + h = -22.978250586 + 24

Combine like terms: -24 + 24 = 0
0 + h = -22.978250586 + 24
h = -22.978250586 + 24

Combine like terms: -22.978250586 + 24 = 1.021749414
h = 1.021749414

Simplifying
h = 1.021749414

Solution
The solution to the problem is based on the solutions
from the subproblems.
h = {46.978250586, 1.021749414}