2g^2-36g+17=0

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Solution for 2g^2-36g+17=0 equation: 


Simplifying
2g2 + -36g + 17 = 0

Reorder the terms:
17 + -36g + 2g2 = 0

Solving
17 + -36g + 2g2 = 0

Solving for variable 'g'.

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

Divide each side by '2'.
8.5 + -18g + g2 = 0

Move the constant term to the right:

Add '-8.5' to each side of the equation.
8.5 + -18g + -8.5 + g2 = 0 + -8.5

Reorder the terms:
8.5 + -8.5 + -18g + g2 = 0 + -8.5

Combine like terms: 8.5 + -8.5 = 0.0
0.0 + -18g + g2 = 0 + -8.5
-18g + g2 = 0 + -8.5

Combine like terms: 0 + -8.5 = -8.5
-18g + g2 = -8.5

The g term is -18g.  Take half its coefficient (-9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
-18g + 81 + g2 = -8.5 + 81

Reorder the terms:
81 + -18g + g2 = -8.5 + 81

Combine like terms: -8.5 + 81 = 72.5
81 + -18g + g2 = 72.5

Factor a perfect square on the left side:
(g + -9)(g + -9) = 72.5

Calculate the square root of the right side: 8.514693183

Break this problem into two subproblems by setting 
(g + -9) equal to 8.514693183 and -8.514693183.


Subproblem 1
g + -9 = 8.514693183

Simplifying
g + -9 = 8.514693183

Reorder the terms:
-9 + g = 8.514693183

Solving
-9 + g = 8.514693183

Solving for variable 'g'.

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

Add '9' to each side of the equation.
-9 + 9 + g = 8.514693183 + 9

Combine like terms: -9 + 9 = 0
0 + g = 8.514693183 + 9
g = 8.514693183 + 9

Combine like terms: 8.514693183 + 9 = 17.514693183
g = 17.514693183

Simplifying
g = 17.514693183


Subproblem 2
g + -9 = -8.514693183

Simplifying
g + -9 = -8.514693183

Reorder the terms:
-9 + g = -8.514693183

Solving
-9 + g = -8.514693183

Solving for variable 'g'.

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

Add '9' to each side of the equation.
-9 + 9 + g = -8.514693183 + 9

Combine like terms: -9 + 9 = 0
0 + g = -8.514693183 + 9
g = -8.514693183 + 9

Combine like terms: -8.514693183 + 9 = 0.485306817
g = 0.485306817

Simplifying
g = 0.485306817


Solution
The solution to the problem is based on the solutions
from the subproblems.
g = {17.514693183, 0.485306817}

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