2g^2+4g-4=0

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Solution for 2g^2+4g-4=0 equation: 


Simplifying
2g2 + 4g + -4 = 0

Reorder the terms:
-4 + 4g + 2g2 = 0

Solving
-4 + 4g + 2g2 = 0

Solving for variable 'g'.

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

Ignore the factor 2.

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

Simplifying
-2 + 2g + g2 = 0

Solving
-2 + 2g + g2 = 0

Begin completing the square.

Move the constant term to the right:

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

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

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

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

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 = 2 + 1

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

Combine like terms: 2 + 1 = 3
1 + 2g + g2 = 3

Factor a perfect square on the left side:
(g + 1)(g + 1) = 3

Calculate the square root of the right side: 1.732050808

Break this problem into two subproblems by setting 
(g + 1) equal to 1.732050808 and -1.732050808.


Subproblem 1
g + 1 = 1.732050808

Simplifying
g + 1 = 1.732050808

Reorder the terms:
1 + g = 1.732050808

Solving
1 + g = 1.732050808

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 = 1.732050808 + -1

Combine like terms: 1 + -1 = 0
0 + g = 1.732050808 + -1
g = 1.732050808 + -1

Combine like terms: 1.732050808 + -1 = 0.732050808
g = 0.732050808

Simplifying
g = 0.732050808


Subproblem 2
g + 1 = -1.732050808

Simplifying
g + 1 = -1.732050808

Reorder the terms:
1 + g = -1.732050808

Solving
1 + g = -1.732050808

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 = -1.732050808 + -1

Combine like terms: 1 + -1 = 0
0 + g = -1.732050808 + -1
g = -1.732050808 + -1

Combine like terms: -1.732050808 + -1 = -2.732050808
g = -2.732050808

Simplifying
g = -2.732050808


Solution
The solution to the problem is based on the solutions
from the subproblems.
g = {0.732050808, -2.732050808}
Solution
g = {0.732050808, -2.732050808}

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