2h^2+8h+2=0

Solution for 2h^2+8h+2=0 equation:

Simplifying
2h2 + 8h + 2 = 0

Reorder the terms:
2 + 8h + 2h2 = 0

Solving
2 + 8h + 2h2 = 0

Solving for variable 'h'.

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + 4h + h2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(1 + 4h + h2)' equal to zero and attempt to solve:

Simplifying
1 + 4h + h2 = 0

Solving
1 + 4h + h2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 4h + -1 + h2 = 0 + -1

Reorder the terms:
1 + -1 + 4h + h2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 4h + h2 = 0 + -1
4h + h2 = 0 + -1

Combine like terms: 0 + -1 = -1
4h + h2 = -1

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 = -1 + 4

Reorder the terms:
4 + 4h + h2 = -1 + 4

Combine like terms: -1 + 4 = 3
4 + 4h + h2 = 3

Factor a perfect square on the left side:
(h + 2)(h + 2) = 3

Calculate the square root of the right side: 1.732050808

Break this problem into two subproblems by setting 
(h + 2) equal to 1.732050808 and -1.732050808.

Subproblem 1
h + 2 = 1.732050808

Simplifying
h + 2 = 1.732050808

Reorder the terms:
2 + h = 1.732050808

Solving
2 + h = 1.732050808

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 = 1.732050808 + -2

Combine like terms: 2 + -2 = 0
0 + h = 1.732050808 + -2
h = 1.732050808 + -2

Combine like terms: 1.732050808 + -2 = -0.267949192
h = -0.267949192

Simplifying
h = -0.267949192

Subproblem 2
h + 2 = -1.732050808

Simplifying
h + 2 = -1.732050808

Reorder the terms:
2 + h = -1.732050808

Solving
2 + h = -1.732050808

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 = -1.732050808 + -2

Combine like terms: 2 + -2 = 0
0 + h = -1.732050808 + -2
h = -1.732050808 + -2

Combine like terms: -1.732050808 + -2 = -3.732050808
h = -3.732050808

Simplifying
h = -3.732050808

Solution
The solution to the problem is based on the solutions
from the subproblems.
h = {-0.267949192, -3.732050808}
Solution
h = {-0.267949192, -3.732050808}