g^2-29g+36=0

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Solution for g^2-29g+36=0 equation:


Simplifying
g2 + -29g + 36 = 0

Reorder the terms:
36 + -29g + g2 = 0

Solving
36 + -29g + g2 = 0

Solving for variable 'g'.

Begin completing the square.

Move the constant term to the right:

Add '-36' to each side of the equation.
36 + -29g + -36 + g2 = 0 + -36

Reorder the terms:
36 + -36 + -29g + g2 = 0 + -36

Combine like terms: 36 + -36 = 0
0 + -29g + g2 = 0 + -36
-29g + g2 = 0 + -36

Combine like terms: 0 + -36 = -36
-29g + g2 = -36

The g term is -29g.  Take half its coefficient (-14.5).
Square it (210.25) and add it to both sides.

Add '210.25' to each side of the equation.
-29g + 210.25 + g2 = -36 + 210.25

Reorder the terms:
210.25 + -29g + g2 = -36 + 210.25

Combine like terms: -36 + 210.25 = 174.25
210.25 + -29g + g2 = 174.25

Factor a perfect square on the left side:
(g + -14.5)(g + -14.5) = 174.25

Calculate the square root of the right side: 13.200378782

Break this problem into two subproblems by setting 
(g + -14.5) equal to 13.200378782 and -13.200378782.


Subproblem 1
g + -14.5 = 13.200378782

Simplifying
g + -14.5 = 13.200378782

Reorder the terms:
-14.5 + g = 13.200378782

Solving
-14.5 + g = 13.200378782

Solving for variable 'g'.

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

Add '14.5' to each side of the equation.
-14.5 + 14.5 + g = 13.200378782 + 14.5

Combine like terms: -14.5 + 14.5 = 0.0
0.0 + g = 13.200378782 + 14.5
g = 13.200378782 + 14.5

Combine like terms: 13.200378782 + 14.5 = 27.700378782
g = 27.700378782

Simplifying
g = 27.700378782


Subproblem 2
g + -14.5 = -13.200378782

Simplifying
g + -14.5 = -13.200378782

Reorder the terms:
-14.5 + g = -13.200378782

Solving
-14.5 + g = -13.200378782

Solving for variable 'g'.

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

Add '14.5' to each side of the equation.
-14.5 + 14.5 + g = -13.200378782 + 14.5

Combine like terms: -14.5 + 14.5 = 0.0
0.0 + g = -13.200378782 + 14.5
g = -13.200378782 + 14.5

Combine like terms: -13.200378782 + 14.5 = 1.299621218
g = 1.299621218

Simplifying
g = 1.299621218


Solution
The solution to the problem is based on the solutions
from the subproblems.
g = {27.700378782, 1.299621218}

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