-2g^2+52g-18=0

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Solution for -2g^2+52g-18=0 equation: 


Simplifying
-2g2 + 52g + -18 = 0

Reorder the terms:
-18 + 52g + -2g2 = 0

Solving
-18 + 52g + -2g2 = 0

Solving for variable 'g'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-9 + 26g + -1g2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-9 + 26g + -1g2)' equal to zero and attempt to solve:

Simplifying
-9 + 26g + -1g2 = 0

Solving
-9 + 26g + -1g2 = 0

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

Divide each side by '-1'.
9 + -26g + g2 = 0

Move the constant term to the right:

Add '-9' to each side of the equation.
9 + -26g + -9 + g2 = 0 + -9

Reorder the terms:
9 + -9 + -26g + g2 = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -26g + g2 = 0 + -9
-26g + g2 = 0 + -9

Combine like terms: 0 + -9 = -9
-26g + g2 = -9

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 = -9 + 169

Reorder the terms:
169 + -26g + g2 = -9 + 169

Combine like terms: -9 + 169 = 160
169 + -26g + g2 = 160

Factor a perfect square on the left side:
(g + -13)(g + -13) = 160

Calculate the square root of the right side: 12.649110641

Break this problem into two subproblems by setting 
(g + -13) equal to 12.649110641 and -12.649110641.


Subproblem 1
g + -13 = 12.649110641

Simplifying
g + -13 = 12.649110641

Reorder the terms:
-13 + g = 12.649110641

Solving
-13 + g = 12.649110641

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 = 12.649110641 + 13

Combine like terms: -13 + 13 = 0
0 + g = 12.649110641 + 13
g = 12.649110641 + 13

Combine like terms: 12.649110641 + 13 = 25.649110641
g = 25.649110641

Simplifying
g = 25.649110641


Subproblem 2
g + -13 = -12.649110641

Simplifying
g + -13 = -12.649110641

Reorder the terms:
-13 + g = -12.649110641

Solving
-13 + g = -12.649110641

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 = -12.649110641 + 13

Combine like terms: -13 + 13 = 0
0 + g = -12.649110641 + 13
g = -12.649110641 + 13

Combine like terms: -12.649110641 + 13 = 0.350889359
g = 0.350889359

Simplifying
g = 0.350889359


Solution
The solution to the problem is based on the solutions
from the subproblems.
g = {25.649110641, 0.350889359}
Solution
g = {25.649110641, 0.350889359}

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