h^2-2h-7=0

Solution for h^2-2h-7=0 equation:

Simplifying
h2 + -2h + -7 = 0

Reorder the terms:
-7 + -2h + h2 = 0

Solving
-7 + -2h + h2 = 0

Solving for variable 'h'.

Begin completing the square.

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + -2h + 7 + h2 = 0 + 7

Reorder the terms:
-7 + 7 + -2h + h2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -2h + h2 = 0 + 7
-2h + h2 = 0 + 7

Combine like terms: 0 + 7 = 7
-2h + h2 = 7

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 = 7 + 1

Reorder the terms:
1 + -2h + h2 = 7 + 1

Combine like terms: 7 + 1 = 8
1 + -2h + h2 = 8

Factor a perfect square on the left side:
(h + -1)(h + -1) = 8

Calculate the square root of the right side: 2.828427125

Break this problem into two subproblems by setting 
(h + -1) equal to 2.828427125 and -2.828427125.

Subproblem 1
h + -1 = 2.828427125

Simplifying
h + -1 = 2.828427125

Reorder the terms:
-1 + h = 2.828427125

Solving
-1 + h = 2.828427125

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 = 2.828427125 + 1

Combine like terms: -1 + 1 = 0
0 + h = 2.828427125 + 1
h = 2.828427125 + 1

Combine like terms: 2.828427125 + 1 = 3.828427125
h = 3.828427125

Simplifying
h = 3.828427125

Subproblem 2
h + -1 = -2.828427125

Simplifying
h + -1 = -2.828427125

Reorder the terms:
-1 + h = -2.828427125

Solving
-1 + h = -2.828427125

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 = -2.828427125 + 1

Combine like terms: -1 + 1 = 0
0 + h = -2.828427125 + 1
h = -2.828427125 + 1

Combine like terms: -2.828427125 + 1 = -1.828427125
h = -1.828427125

Simplifying
h = -1.828427125

Solution
The solution to the problem is based on the solutions
from the subproblems.
h = {3.828427125, -1.828427125}