h^2-4h-27=0

Solution for h^2-4h-27=0 equation:

Simplifying
h2 + -4h + -27 = 0

Reorder the terms:
-27 + -4h + h2 = 0

Solving
-27 + -4h + h2 = 0

Solving for variable 'h'.

Begin completing the square.

Move the constant term to the right:

Add '27' to each side of the equation.
-27 + -4h + 27 + h2 = 0 + 27

Reorder the terms:
-27 + 27 + -4h + h2 = 0 + 27

Combine like terms: -27 + 27 = 0
0 + -4h + h2 = 0 + 27
-4h + h2 = 0 + 27

Combine like terms: 0 + 27 = 27
-4h + h2 = 27

The h term is -4h.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4h + 4 + h2 = 27 + 4

Reorder the terms:
4 + -4h + h2 = 27 + 4

Combine like terms: 27 + 4 = 31
4 + -4h + h2 = 31

Factor a perfect square on the left side:
(h + -2)(h + -2) = 31

Calculate the square root of the right side: 5.567764363

Break this problem into two subproblems by setting 
(h + -2) equal to 5.567764363 and -5.567764363.

Subproblem 1
h + -2 = 5.567764363

Simplifying
h + -2 = 5.567764363

Reorder the terms:
-2 + h = 5.567764363

Solving
-2 + h = 5.567764363

Solving for variable 'h'.

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

Add '2' to each side of the equation.
-2 + 2 + h = 5.567764363 + 2

Combine like terms: -2 + 2 = 0
0 + h = 5.567764363 + 2
h = 5.567764363 + 2

Combine like terms: 5.567764363 + 2 = 7.567764363
h = 7.567764363

Simplifying
h = 7.567764363

Subproblem 2
h + -2 = -5.567764363

Simplifying
h + -2 = -5.567764363

Reorder the terms:
-2 + h = -5.567764363

Solving
-2 + h = -5.567764363

Solving for variable 'h'.

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

Add '2' to each side of the equation.
-2 + 2 + h = -5.567764363 + 2

Combine like terms: -2 + 2 = 0
0 + h = -5.567764363 + 2
h = -5.567764363 + 2

Combine like terms: -5.567764363 + 2 = -3.567764363
h = -3.567764363

Simplifying
h = -3.567764363

Solution
The solution to the problem is based on the solutions
from the subproblems.
h = {7.567764363, -3.567764363}