-2g^2+52g-82=0

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Solution for -2g^2+52g-82=0 equation: 


Simplifying
-2g2 + 52g + -82 = 0

Reorder the terms:
-82 + 52g + -2g2 = 0

Solving
-82 + 52g + -2g2 = 0

Solving for variable 'g'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-41 + 26g + -1g2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-41 + 26g + -1g2)' equal to zero and attempt to solve:

Simplifying
-41 + 26g + -1g2 = 0

Solving
-41 + 26g + -1g2 = 0

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

Divide each side by '-1'.
41 + -26g + g2 = 0

Move the constant term to the right:

Add '-41' to each side of the equation.
41 + -26g + -41 + g2 = 0 + -41

Reorder the terms:
41 + -41 + -26g + g2 = 0 + -41

Combine like terms: 41 + -41 = 0
0 + -26g + g2 = 0 + -41
-26g + g2 = 0 + -41

Combine like terms: 0 + -41 = -41
-26g + g2 = -41

The g term is -26g.  Take half its coefficient (-13).
Square it (169) and add it to both sides.

Add '169' to each side of the equation.
-26g + 169 + g2 = -41 + 169

Reorder the terms:
169 + -26g + g2 = -41 + 169

Combine like terms: -41 + 169 = 128
169 + -26g + g2 = 128

Factor a perfect square on the left side:
(g + -13)(g + -13) = 128

Calculate the square root of the right side: 11.313708499

Break this problem into two subproblems by setting 
(g + -13) equal to 11.313708499 and -11.313708499.


Subproblem 1
g + -13 = 11.313708499

Simplifying
g + -13 = 11.313708499

Reorder the terms:
-13 + g = 11.313708499

Solving
-13 + g = 11.313708499

Solving for variable 'g'.

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

Add '13' to each side of the equation.
-13 + 13 + g = 11.313708499 + 13

Combine like terms: -13 + 13 = 0
0 + g = 11.313708499 + 13
g = 11.313708499 + 13

Combine like terms: 11.313708499 + 13 = 24.313708499
g = 24.313708499

Simplifying
g = 24.313708499


Subproblem 2
g + -13 = -11.313708499

Simplifying
g + -13 = -11.313708499

Reorder the terms:
-13 + g = -11.313708499

Solving
-13 + g = -11.313708499

Solving for variable 'g'.

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

Add '13' to each side of the equation.
-13 + 13 + g = -11.313708499 + 13

Combine like terms: -13 + 13 = 0
0 + g = -11.313708499 + 13
g = -11.313708499 + 13

Combine like terms: -11.313708499 + 13 = 1.686291501
g = 1.686291501

Simplifying
g = 1.686291501


Solution
The solution to the problem is based on the solutions
from the subproblems.
g = {24.313708499, 1.686291501}
Solution
g = {24.313708499, 1.686291501}

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