7(g^2-2g-2g-4)=0

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Solution for 7(g^2-2g-2g-4)=0 equation: 


Simplifying
7(g2 + -2g + -2g + -4) = 0

Reorder the terms:
7(-4 + -2g + -2g + g2) = 0

Combine like terms: -2g + -2g = -4g
7(-4 + -4g + g2) = 0
(-4 * 7 + -4g * 7 + g2 * 7) = 0
(-28 + -28g + 7g2) = 0

Solving
-28 + -28g + 7g2 = 0

Solving for variable 'g'.

Factor out the Greatest Common Factor (GCF), '7'.
7(-4 + -4g + g2) = 0

Ignore the factor 7.

Subproblem 1
Set the factor '(-4 + -4g + g2)' equal to zero and attempt to solve:

Simplifying
-4 + -4g + g2 = 0

Solving
-4 + -4g + g2 = 0

Begin completing the square.

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + -4g + 4 + g2 = 0 + 4

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

Combine like terms: -4 + 4 = 0
0 + -4g + g2 = 0 + 4
-4g + g2 = 0 + 4

Combine like terms: 0 + 4 = 4
-4g + g2 = 4

The g term is -4g.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4g + 4 + g2 = 4 + 4

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

Combine like terms: 4 + 4 = 8
4 + -4g + g2 = 8

Factor a perfect square on the left side:
(g + -2)(g + -2) = 8

Calculate the square root of the right side: 2.828427125

Break this problem into two subproblems by setting 
(g + -2) equal to 2.828427125 and -2.828427125.


Subproblem 1
g + -2 = 2.828427125

Simplifying
g + -2 = 2.828427125

Reorder the terms:
-2 + g = 2.828427125

Solving
-2 + g = 2.828427125

Solving for variable 'g'.

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

Add '2' to each side of the equation.
-2 + 2 + g = 2.828427125 + 2

Combine like terms: -2 + 2 = 0
0 + g = 2.828427125 + 2
g = 2.828427125 + 2

Combine like terms: 2.828427125 + 2 = 4.828427125
g = 4.828427125

Simplifying
g = 4.828427125


Subproblem 2
g + -2 = -2.828427125

Simplifying
g + -2 = -2.828427125

Reorder the terms:
-2 + g = -2.828427125

Solving
-2 + g = -2.828427125

Solving for variable 'g'.

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

Add '2' to each side of the equation.
-2 + 2 + g = -2.828427125 + 2

Combine like terms: -2 + 2 = 0
0 + g = -2.828427125 + 2
g = -2.828427125 + 2

Combine like terms: -2.828427125 + 2 = -0.828427125
g = -0.828427125

Simplifying
g = -0.828427125


Solution
The solution to the problem is based on the solutions
from the subproblems.
g = {4.828427125, -0.828427125}
Solution
g = {4.828427125, -0.828427125}

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