9g^2-126g+27=0

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Solution for 9g^2-126g+27=0 equation: 


Simplifying
9g2 + -126g + 27 = 0

Reorder the terms:
27 + -126g + 9g2 = 0

Solving
27 + -126g + 9g2 = 0

Solving for variable 'g'.

Factor out the Greatest Common Factor (GCF), '9'.
9(3 + -14g + g2) = 0

Ignore the factor 9.

Subproblem 1
Set the factor '(3 + -14g + g2)' equal to zero and attempt to solve:

Simplifying
3 + -14g + g2 = 0

Solving
3 + -14g + g2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + -14g + -3 + g2 = 0 + -3

Reorder the terms:
3 + -3 + -14g + g2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -14g + g2 = 0 + -3
-14g + g2 = 0 + -3

Combine like terms: 0 + -3 = -3
-14g + g2 = -3

The g term is -14g.  Take half its coefficient (-7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
-14g + 49 + g2 = -3 + 49

Reorder the terms:
49 + -14g + g2 = -3 + 49

Combine like terms: -3 + 49 = 46
49 + -14g + g2 = 46

Factor a perfect square on the left side:
(g + -7)(g + -7) = 46

Calculate the square root of the right side: 6.782329983

Break this problem into two subproblems by setting 
(g + -7) equal to 6.782329983 and -6.782329983.


Subproblem 1
g + -7 = 6.782329983

Simplifying
g + -7 = 6.782329983

Reorder the terms:
-7 + g = 6.782329983

Solving
-7 + g = 6.782329983

Solving for variable 'g'.

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

Add '7' to each side of the equation.
-7 + 7 + g = 6.782329983 + 7

Combine like terms: -7 + 7 = 0
0 + g = 6.782329983 + 7
g = 6.782329983 + 7

Combine like terms: 6.782329983 + 7 = 13.782329983
g = 13.782329983

Simplifying
g = 13.782329983


Subproblem 2
g + -7 = -6.782329983

Simplifying
g + -7 = -6.782329983

Reorder the terms:
-7 + g = -6.782329983

Solving
-7 + g = -6.782329983

Solving for variable 'g'.

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

Add '7' to each side of the equation.
-7 + 7 + g = -6.782329983 + 7

Combine like terms: -7 + 7 = 0
0 + g = -6.782329983 + 7
g = -6.782329983 + 7

Combine like terms: -6.782329983 + 7 = 0.217670017
g = 0.217670017

Simplifying
g = 0.217670017


Solution
The solution to the problem is based on the solutions
from the subproblems.
g = {13.782329983, 0.217670017}
Solution
g = {13.782329983, 0.217670017}

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