g^2-16g+10=0

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Solution for g^2-16g+10=0 equation: 


Simplifying
g2 + -16g + 10 = 0

Reorder the terms:
10 + -16g + g2 = 0

Solving
10 + -16g + 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 + -16g + -10 + g2 = 0 + -10

Reorder the terms:
10 + -10 + -16g + g2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -16g + g2 = 0 + -10
-16g + g2 = 0 + -10

Combine like terms: 0 + -10 = -10
-16g + g2 = -10

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 = -10 + 64

Reorder the terms:
64 + -16g + g2 = -10 + 64

Combine like terms: -10 + 64 = 54
64 + -16g + g2 = 54

Factor a perfect square on the left side:
(g + -8)(g + -8) = 54

Calculate the square root of the right side: 7.348469228

Break this problem into two subproblems by setting 
(g + -8) equal to 7.348469228 and -7.348469228.


Subproblem 1
g + -8 = 7.348469228

Simplifying
g + -8 = 7.348469228

Reorder the terms:
-8 + g = 7.348469228

Solving
-8 + g = 7.348469228

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 = 7.348469228 + 8

Combine like terms: -8 + 8 = 0
0 + g = 7.348469228 + 8
g = 7.348469228 + 8

Combine like terms: 7.348469228 + 8 = 15.348469228
g = 15.348469228

Simplifying
g = 15.348469228


Subproblem 2
g + -8 = -7.348469228

Simplifying
g + -8 = -7.348469228

Reorder the terms:
-8 + g = -7.348469228

Solving
-8 + g = -7.348469228

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 = -7.348469228 + 8

Combine like terms: -8 + 8 = 0
0 + g = -7.348469228 + 8
g = -7.348469228 + 8

Combine like terms: -7.348469228 + 8 = 0.651530772
g = 0.651530772

Simplifying
g = 0.651530772


Solution
The solution to the problem is based on the solutions
from the subproblems.
g = {15.348469228, 0.651530772}

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