g^2+16g+17=0

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Solution for g^2+16g+17=0 equation: 


Simplifying
g2 + 16g + 17 = 0

Reorder the terms:
17 + 16g + g2 = 0

Solving
17 + 16g + g2 = 0

Solving for variable 'g'.

Begin completing the square.

Move the constant term to the right:

Add '-17' to each side of the equation.
17 + 16g + -17 + g2 = 0 + -17

Reorder the terms:
17 + -17 + 16g + g2 = 0 + -17

Combine like terms: 17 + -17 = 0
0 + 16g + g2 = 0 + -17
16g + g2 = 0 + -17

Combine like terms: 0 + -17 = -17
16g + g2 = -17

The g term is 16g.  Take half its coefficient (8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
16g + 64 + g2 = -17 + 64

Reorder the terms:
64 + 16g + g2 = -17 + 64

Combine like terms: -17 + 64 = 47
64 + 16g + g2 = 47

Factor a perfect square on the left side:
(g + 8)(g + 8) = 47

Calculate the square root of the right side: 6.8556546

Break this problem into two subproblems by setting 
(g + 8) equal to 6.8556546 and -6.8556546.


Subproblem 1
g + 8 = 6.8556546

Simplifying
g + 8 = 6.8556546

Reorder the terms:
8 + g = 6.8556546

Solving
8 + g = 6.8556546

Solving for variable 'g'.

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

Add '-8' to each side of the equation.
8 + -8 + g = 6.8556546 + -8

Combine like terms: 8 + -8 = 0
0 + g = 6.8556546 + -8
g = 6.8556546 + -8

Combine like terms: 6.8556546 + -8 = -1.1443454
g = -1.1443454

Simplifying
g = -1.1443454


Subproblem 2
g + 8 = -6.8556546

Simplifying
g + 8 = -6.8556546

Reorder the terms:
8 + g = -6.8556546

Solving
8 + g = -6.8556546

Solving for variable 'g'.

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

Add '-8' to each side of the equation.
8 + -8 + g = -6.8556546 + -8

Combine like terms: 8 + -8 = 0
0 + g = -6.8556546 + -8
g = -6.8556546 + -8

Combine like terms: -6.8556546 + -8 = -14.8556546
g = -14.8556546

Simplifying
g = -14.8556546


Solution
The solution to the problem is based on the solutions
from the subproblems.
g = {-1.1443454, -14.8556546}

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