3g^2+87g+81=0

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Solution for 3g^2+87g+81=0 equation: 


Simplifying
3g2 + 87g + 81 = 0

Reorder the terms:
81 + 87g + 3g2 = 0

Solving
81 + 87g + 3g2 = 0

Solving for variable 'g'.

Factor out the Greatest Common Factor (GCF), '3'.
3(27 + 29g + g2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(27 + 29g + g2)' equal to zero and attempt to solve:

Simplifying
27 + 29g + g2 = 0

Solving
27 + 29g + g2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-27' to each side of the equation.
27 + 29g + -27 + g2 = 0 + -27

Reorder the terms:
27 + -27 + 29g + g2 = 0 + -27

Combine like terms: 27 + -27 = 0
0 + 29g + g2 = 0 + -27
29g + g2 = 0 + -27

Combine like terms: 0 + -27 = -27
29g + g2 = -27

The g term is 29g.  Take half its coefficient (14.5).
Square it (210.25) and add it to both sides.

Add '210.25' to each side of the equation.
29g + 210.25 + g2 = -27 + 210.25

Reorder the terms:
210.25 + 29g + g2 = -27 + 210.25

Combine like terms: -27 + 210.25 = 183.25
210.25 + 29g + g2 = 183.25

Factor a perfect square on the left side:
(g + 14.5)(g + 14.5) = 183.25

Calculate the square root of the right side: 13.536986371

Break this problem into two subproblems by setting 
(g + 14.5) equal to 13.536986371 and -13.536986371.


Subproblem 1
g + 14.5 = 13.536986371

Simplifying
g + 14.5 = 13.536986371

Reorder the terms:
14.5 + g = 13.536986371

Solving
14.5 + g = 13.536986371

Solving for variable 'g'.

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

Add '-14.5' to each side of the equation.
14.5 + -14.5 + g = 13.536986371 + -14.5

Combine like terms: 14.5 + -14.5 = 0.0
0.0 + g = 13.536986371 + -14.5
g = 13.536986371 + -14.5

Combine like terms: 13.536986371 + -14.5 = -0.963013629
g = -0.963013629

Simplifying
g = -0.963013629


Subproblem 2
g + 14.5 = -13.536986371

Simplifying
g + 14.5 = -13.536986371

Reorder the terms:
14.5 + g = -13.536986371

Solving
14.5 + g = -13.536986371

Solving for variable 'g'.

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

Add '-14.5' to each side of the equation.
14.5 + -14.5 + g = -13.536986371 + -14.5

Combine like terms: 14.5 + -14.5 = 0.0
0.0 + g = -13.536986371 + -14.5
g = -13.536986371 + -14.5

Combine like terms: -13.536986371 + -14.5 = -28.036986371
g = -28.036986371

Simplifying
g = -28.036986371


Solution
The solution to the problem is based on the solutions
from the subproblems.
g = {-0.963013629, -28.036986371}
Solution
g = {-0.963013629, -28.036986371}

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