8g^2+16g-8=0

Solution for 8g^2+16g-8=0 equation:

Simplifying
8g2 + 16g + -8 = 0

Reorder the terms:
-8 + 16g + 8g2 = 0

Solving
-8 + 16g + 8g2 = 0

Solving for variable 'g'.

Factor out the Greatest Common Factor (GCF), '8'.
8(-1 + 2g + g2) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(-1 + 2g + g2)' equal to zero and attempt to solve:

Simplifying
-1 + 2g + g2 = 0

Solving
-1 + 2g + g2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 2g + 1 + g2 = 0 + 1

Reorder the terms:
-1 + 1 + 2g + g2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 2g + g2 = 0 + 1
2g + g2 = 0 + 1

Combine like terms: 0 + 1 = 1
2g + g2 = 1

The g term is 2g.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2g + 1 + g2 = 1 + 1

Reorder the terms:
1 + 2g + g2 = 1 + 1

Combine like terms: 1 + 1 = 2
1 + 2g + g2 = 2

Factor a perfect square on the left side:
(g + 1)(g + 1) = 2

Calculate the square root of the right side: 1.414213562

Break this problem into two subproblems by setting 
(g + 1) equal to 1.414213562 and -1.414213562.

Subproblem 1
g + 1 = 1.414213562

Simplifying
g + 1 = 1.414213562

Reorder the terms:
1 + g = 1.414213562

Solving
1 + g = 1.414213562

Solving for variable 'g'.

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

Add '-1' to each side of the equation.
1 + -1 + g = 1.414213562 + -1

Combine like terms: 1 + -1 = 0
0 + g = 1.414213562 + -1
g = 1.414213562 + -1

Combine like terms: 1.414213562 + -1 = 0.414213562
g = 0.414213562

Simplifying
g = 0.414213562

Subproblem 2
g + 1 = -1.414213562

Simplifying
g + 1 = -1.414213562

Reorder the terms:
1 + g = -1.414213562

Solving
1 + g = -1.414213562

Solving for variable 'g'.

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

Add '-1' to each side of the equation.
1 + -1 + g = -1.414213562 + -1

Combine like terms: 1 + -1 = 0
0 + g = -1.414213562 + -1
g = -1.414213562 + -1

Combine like terms: -1.414213562 + -1 = -2.414213562
g = -2.414213562

Simplifying
g = -2.414213562

Solution
The solution to the problem is based on the solutions
from the subproblems.
g = {0.414213562, -2.414213562}
Solution
g = {0.414213562, -2.414213562}