-10g^2-54g+130=0

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Solution for -10g^2-54g+130=0 equation: 


Simplifying
-10g2 + -54g + 130 = 0

Reorder the terms:
130 + -54g + -10g2 = 0

Solving
130 + -54g + -10g2 = 0

Solving for variable 'g'.

Factor out the Greatest Common Factor (GCF), '2'.
2(65 + -27g + -5g2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(65 + -27g + -5g2)' equal to zero and attempt to solve:

Simplifying
65 + -27g + -5g2 = 0

Solving
65 + -27g + -5g2 = 0

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
-13 + 5.4g + g2 = 0

Move the constant term to the right:

Add '13' to each side of the equation.
-13 + 5.4g + 13 + g2 = 0 + 13

Reorder the terms:
-13 + 13 + 5.4g + g2 = 0 + 13

Combine like terms: -13 + 13 = 0
0 + 5.4g + g2 = 0 + 13
5.4g + g2 = 0 + 13

Combine like terms: 0 + 13 = 13
5.4g + g2 = 13

The g term is 5.4g.  Take half its coefficient (2.7).
Square it (7.29) and add it to both sides.

Add '7.29' to each side of the equation.
5.4g + 7.29 + g2 = 13 + 7.29

Reorder the terms:
7.29 + 5.4g + g2 = 13 + 7.29

Combine like terms: 13 + 7.29 = 20.29
7.29 + 5.4g + g2 = 20.29

Factor a perfect square on the left side:
(g + 2.7)(g + 2.7) = 20.29

Calculate the square root of the right side: 4.504442252

Break this problem into two subproblems by setting 
(g + 2.7) equal to 4.504442252 and -4.504442252.


Subproblem 1
g + 2.7 = 4.504442252

Simplifying
g + 2.7 = 4.504442252

Reorder the terms:
2.7 + g = 4.504442252

Solving
2.7 + g = 4.504442252

Solving for variable 'g'.

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

Add '-2.7' to each side of the equation.
2.7 + -2.7 + g = 4.504442252 + -2.7

Combine like terms: 2.7 + -2.7 = 0.0
0.0 + g = 4.504442252 + -2.7
g = 4.504442252 + -2.7

Combine like terms: 4.504442252 + -2.7 = 1.804442252
g = 1.804442252

Simplifying
g = 1.804442252


Subproblem 2
g + 2.7 = -4.504442252

Simplifying
g + 2.7 = -4.504442252

Reorder the terms:
2.7 + g = -4.504442252

Solving
2.7 + g = -4.504442252

Solving for variable 'g'.

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

Add '-2.7' to each side of the equation.
2.7 + -2.7 + g = -4.504442252 + -2.7

Combine like terms: 2.7 + -2.7 = 0.0
0.0 + g = -4.504442252 + -2.7
g = -4.504442252 + -2.7

Combine like terms: -4.504442252 + -2.7 = -7.204442252
g = -7.204442252

Simplifying
g = -7.204442252


Solution
The solution to the problem is based on the solutions
from the subproblems.
g = {1.804442252, -7.204442252}
Solution
g = {1.804442252, -7.204442252}

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