h^2-2h-47=0

Solution for h^2-2h-47=0 equation:

Simplifying
h2 + -2h + -47 = 0

Reorder the terms:
-47 + -2h + h2 = 0

Solving
-47 + -2h + h2 = 0

Solving for variable 'h'.

Begin completing the square.

Move the constant term to the right:

Add '47' to each side of the equation.
-47 + -2h + 47 + h2 = 0 + 47

Reorder the terms:
-47 + 47 + -2h + h2 = 0 + 47

Combine like terms: -47 + 47 = 0
0 + -2h + h2 = 0 + 47
-2h + h2 = 0 + 47

Combine like terms: 0 + 47 = 47
-2h + h2 = 47

The h term is -2h.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2h + 1 + h2 = 47 + 1

Reorder the terms:
1 + -2h + h2 = 47 + 1

Combine like terms: 47 + 1 = 48
1 + -2h + h2 = 48

Factor a perfect square on the left side:
(h + -1)(h + -1) = 48

Calculate the square root of the right side: 6.92820323

Break this problem into two subproblems by setting 
(h + -1) equal to 6.92820323 and -6.92820323.

Subproblem 1
h + -1 = 6.92820323

Simplifying
h + -1 = 6.92820323

Reorder the terms:
-1 + h = 6.92820323

Solving
-1 + h = 6.92820323

Solving for variable 'h'.

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

Add '1' to each side of the equation.
-1 + 1 + h = 6.92820323 + 1

Combine like terms: -1 + 1 = 0
0 + h = 6.92820323 + 1
h = 6.92820323 + 1

Combine like terms: 6.92820323 + 1 = 7.92820323
h = 7.92820323

Simplifying
h = 7.92820323

Subproblem 2
h + -1 = -6.92820323

Simplifying
h + -1 = -6.92820323

Reorder the terms:
-1 + h = -6.92820323

Solving
-1 + h = -6.92820323

Solving for variable 'h'.

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

Add '1' to each side of the equation.
-1 + 1 + h = -6.92820323 + 1

Combine like terms: -1 + 1 = 0
0 + h = -6.92820323 + 1
h = -6.92820323 + 1

Combine like terms: -6.92820323 + 1 = -5.92820323
h = -5.92820323

Simplifying
h = -5.92820323

Solution
The solution to the problem is based on the solutions
from the subproblems.
h = {7.92820323, -5.92820323}