-2g^2-54g+50=0

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Solution for -2g^2-54g+50=0 equation: 


Simplifying
-2g2 + -54g + 50 = 0

Reorder the terms:
50 + -54g + -2g2 = 0

Solving
50 + -54g + -2g2 = 0

Solving for variable 'g'.

Factor out the Greatest Common Factor (GCF), '2'.
2(25 + -27g + -1g2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(25 + -27g + -1g2)' equal to zero and attempt to solve:

Simplifying
25 + -27g + -1g2 = 0

Solving
25 + -27g + -1g2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-25 + 27g + g2 = 0

Move the constant term to the right:

Add '25' to each side of the equation.
-25 + 27g + 25 + g2 = 0 + 25

Reorder the terms:
-25 + 25 + 27g + g2 = 0 + 25

Combine like terms: -25 + 25 = 0
0 + 27g + g2 = 0 + 25
27g + g2 = 0 + 25

Combine like terms: 0 + 25 = 25
27g + g2 = 25

The g term is 27g.  Take half its coefficient (13.5).
Square it (182.25) and add it to both sides.

Add '182.25' to each side of the equation.
27g + 182.25 + g2 = 25 + 182.25

Reorder the terms:
182.25 + 27g + g2 = 25 + 182.25

Combine like terms: 25 + 182.25 = 207.25
182.25 + 27g + g2 = 207.25

Factor a perfect square on the left side:
(g + 13.5)(g + 13.5) = 207.25

Calculate the square root of the right side: 14.396180049

Break this problem into two subproblems by setting 
(g + 13.5) equal to 14.396180049 and -14.396180049.


Subproblem 1
g + 13.5 = 14.396180049

Simplifying
g + 13.5 = 14.396180049

Reorder the terms:
13.5 + g = 14.396180049

Solving
13.5 + g = 14.396180049

Solving for variable 'g'.

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

Add '-13.5' to each side of the equation.
13.5 + -13.5 + g = 14.396180049 + -13.5

Combine like terms: 13.5 + -13.5 = 0.0
0.0 + g = 14.396180049 + -13.5
g = 14.396180049 + -13.5

Combine like terms: 14.396180049 + -13.5 = 0.896180049
g = 0.896180049

Simplifying
g = 0.896180049


Subproblem 2
g + 13.5 = -14.396180049

Simplifying
g + 13.5 = -14.396180049

Reorder the terms:
13.5 + g = -14.396180049

Solving
13.5 + g = -14.396180049

Solving for variable 'g'.

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

Add '-13.5' to each side of the equation.
13.5 + -13.5 + g = -14.396180049 + -13.5

Combine like terms: 13.5 + -13.5 = 0.0
0.0 + g = -14.396180049 + -13.5
g = -14.396180049 + -13.5

Combine like terms: -14.396180049 + -13.5 = -27.896180049
g = -27.896180049

Simplifying
g = -27.896180049


Solution
The solution to the problem is based on the solutions
from the subproblems.
g = {0.896180049, -27.896180049}
Solution
g = {0.896180049, -27.896180049}

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