h^2-22h=43

Solution for h^2-22h=43 equation:

Simplifying
h2 + -22h = 43

Reorder the terms:
-22h + h2 = 43

Solving
-22h + h2 = 43

Solving for variable 'h'.

Reorder the terms:
-43 + -22h + h2 = 43 + -43

Combine like terms: 43 + -43 = 0
-43 + -22h + h2 = 0

Begin completing the square.

Move the constant term to the right:

Add '43' to each side of the equation.
-43 + -22h + 43 + h2 = 0 + 43

Reorder the terms:
-43 + 43 + -22h + h2 = 0 + 43

Combine like terms: -43 + 43 = 0
0 + -22h + h2 = 0 + 43
-22h + h2 = 0 + 43

Combine like terms: 0 + 43 = 43
-22h + h2 = 43

The h term is -22h.  Take half its coefficient (-11).
Square it (121) and add it to both sides.

Add '121' to each side of the equation.
-22h + 121 + h2 = 43 + 121

Reorder the terms:
121 + -22h + h2 = 43 + 121

Combine like terms: 43 + 121 = 164
121 + -22h + h2 = 164

Factor a perfect square on the left side:
(h + -11)(h + -11) = 164

Calculate the square root of the right side: 12.806248475

Break this problem into two subproblems by setting 
(h + -11) equal to 12.806248475 and -12.806248475.

Subproblem 1
h + -11 = 12.806248475

Simplifying
h + -11 = 12.806248475

Reorder the terms:
-11 + h = 12.806248475

Solving
-11 + h = 12.806248475

Solving for variable 'h'.

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

Add '11' to each side of the equation.
-11 + 11 + h = 12.806248475 + 11

Combine like terms: -11 + 11 = 0
0 + h = 12.806248475 + 11
h = 12.806248475 + 11

Combine like terms: 12.806248475 + 11 = 23.806248475
h = 23.806248475

Simplifying
h = 23.806248475

Subproblem 2
h + -11 = -12.806248475

Simplifying
h + -11 = -12.806248475

Reorder the terms:
-11 + h = -12.806248475

Solving
-11 + h = -12.806248475

Solving for variable 'h'.

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

Add '11' to each side of the equation.
-11 + 11 + h = -12.806248475 + 11

Combine like terms: -11 + 11 = 0
0 + h = -12.806248475 + 11
h = -12.806248475 + 11

Combine like terms: -12.806248475 + 11 = -1.806248475
h = -1.806248475

Simplifying
h = -1.806248475

Solution
The solution to the problem is based on the solutions
from the subproblems.
h = {23.806248475, -1.806248475}