g^2+29g+10=0

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Solution for g^2+29g+10=0 equation: 


Simplifying
g2 + 29g + 10 = 0

Reorder the terms:
10 + 29g + g2 = 0

Solving
10 + 29g + g2 = 0

Solving for variable 'g'.

Begin completing the square.

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + 29g + -10 + g2 = 0 + -10

Reorder the terms:
10 + -10 + 29g + g2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + 29g + g2 = 0 + -10
29g + g2 = 0 + -10

Combine like terms: 0 + -10 = -10
29g + g2 = -10

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 = -10 + 210.25

Reorder the terms:
210.25 + 29g + g2 = -10 + 210.25

Combine like terms: -10 + 210.25 = 200.25
210.25 + 29g + g2 = 200.25

Factor a perfect square on the left side:
(g + 14.5)(g + 14.5) = 200.25

Calculate the square root of the right side: 14.150971698

Break this problem into two subproblems by setting 
(g + 14.5) equal to 14.150971698 and -14.150971698.


Subproblem 1
g + 14.5 = 14.150971698

Simplifying
g + 14.5 = 14.150971698

Reorder the terms:
14.5 + g = 14.150971698

Solving
14.5 + g = 14.150971698

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 = 14.150971698 + -14.5

Combine like terms: 14.5 + -14.5 = 0.0
0.0 + g = 14.150971698 + -14.5
g = 14.150971698 + -14.5

Combine like terms: 14.150971698 + -14.5 = -0.349028302
g = -0.349028302

Simplifying
g = -0.349028302


Subproblem 2
g + 14.5 = -14.150971698

Simplifying
g + 14.5 = -14.150971698

Reorder the terms:
14.5 + g = -14.150971698

Solving
14.5 + g = -14.150971698

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 = -14.150971698 + -14.5

Combine like terms: 14.5 + -14.5 = 0.0
0.0 + g = -14.150971698 + -14.5
g = -14.150971698 + -14.5

Combine like terms: -14.150971698 + -14.5 = -28.650971698
g = -28.650971698

Simplifying
g = -28.650971698


Solution
The solution to the problem is based on the solutions
from the subproblems.
g = {-0.349028302, -28.650971698}

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