-h^2-8h-1=0

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Solution for -h^2-8h-1=0 equation: 


Simplifying
-1h2 + -8h + -1 = 0

Reorder the terms:
-1 + -8h + -1h2 = 0

Solving
-1 + -8h + -1h2 = 0

Solving for variable 'h'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(1 + 8h + h2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(1 + 8h + h2)' equal to zero and attempt to solve:

Simplifying
1 + 8h + h2 = 0

Solving
1 + 8h + h2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 8h + -1 + h2 = 0 + -1

Reorder the terms:
1 + -1 + 8h + h2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 8h + h2 = 0 + -1
8h + h2 = 0 + -1

Combine like terms: 0 + -1 = -1
8h + h2 = -1

The h term is 8h.  Take half its coefficient (4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
8h + 16 + h2 = -1 + 16

Reorder the terms:
16 + 8h + h2 = -1 + 16

Combine like terms: -1 + 16 = 15
16 + 8h + h2 = 15

Factor a perfect square on the left side:
(h + 4)(h + 4) = 15

Calculate the square root of the right side: 3.872983346

Break this problem into two subproblems by setting 
(h + 4) equal to 3.872983346 and -3.872983346.


Subproblem 1
h + 4 = 3.872983346

Simplifying
h + 4 = 3.872983346

Reorder the terms:
4 + h = 3.872983346

Solving
4 + h = 3.872983346

Solving for variable 'h'.

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

Add '-4' to each side of the equation.
4 + -4 + h = 3.872983346 + -4

Combine like terms: 4 + -4 = 0
0 + h = 3.872983346 + -4
h = 3.872983346 + -4

Combine like terms: 3.872983346 + -4 = -0.127016654
h = -0.127016654

Simplifying
h = -0.127016654


Subproblem 2
h + 4 = -3.872983346

Simplifying
h + 4 = -3.872983346

Reorder the terms:
4 + h = -3.872983346

Solving
4 + h = -3.872983346

Solving for variable 'h'.

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

Add '-4' to each side of the equation.
4 + -4 + h = -3.872983346 + -4

Combine like terms: 4 + -4 = 0
0 + h = -3.872983346 + -4
h = -3.872983346 + -4

Combine like terms: -3.872983346 + -4 = -7.872983346
h = -7.872983346

Simplifying
h = -7.872983346


Solution
The solution to the problem is based on the solutions
from the subproblems.
h = {-0.127016654, -7.872983346}
Solution
h = {-0.127016654, -7.872983346}

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