g^2-19g+9=0

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Solution for g^2-19g+9=0 equation: 


Simplifying
g2 + -19g + 9 = 0

Reorder the terms:
9 + -19g + g2 = 0

Solving
9 + -19g + g2 = 0

Solving for variable 'g'.

Begin completing the square.

Move the constant term to the right:

Add '-9' to each side of the equation.
9 + -19g + -9 + g2 = 0 + -9

Reorder the terms:
9 + -9 + -19g + g2 = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -19g + g2 = 0 + -9
-19g + g2 = 0 + -9

Combine like terms: 0 + -9 = -9
-19g + g2 = -9

The g term is -19g.  Take half its coefficient (-9.5).
Square it (90.25) and add it to both sides.

Add '90.25' to each side of the equation.
-19g + 90.25 + g2 = -9 + 90.25

Reorder the terms:
90.25 + -19g + g2 = -9 + 90.25

Combine like terms: -9 + 90.25 = 81.25
90.25 + -19g + g2 = 81.25

Factor a perfect square on the left side:
(g + -9.5)(g + -9.5) = 81.25

Calculate the square root of the right side: 9.013878189

Break this problem into two subproblems by setting 
(g + -9.5) equal to 9.013878189 and -9.013878189.


Subproblem 1
g + -9.5 = 9.013878189

Simplifying
g + -9.5 = 9.013878189

Reorder the terms:
-9.5 + g = 9.013878189

Solving
-9.5 + g = 9.013878189

Solving for variable 'g'.

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

Add '9.5' to each side of the equation.
-9.5 + 9.5 + g = 9.013878189 + 9.5

Combine like terms: -9.5 + 9.5 = 0.0
0.0 + g = 9.013878189 + 9.5
g = 9.013878189 + 9.5

Combine like terms: 9.013878189 + 9.5 = 18.513878189
g = 18.513878189

Simplifying
g = 18.513878189


Subproblem 2
g + -9.5 = -9.013878189

Simplifying
g + -9.5 = -9.013878189

Reorder the terms:
-9.5 + g = -9.013878189

Solving
-9.5 + g = -9.013878189

Solving for variable 'g'.

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

Add '9.5' to each side of the equation.
-9.5 + 9.5 + g = -9.013878189 + 9.5

Combine like terms: -9.5 + 9.5 = 0.0
0.0 + g = -9.013878189 + 9.5
g = -9.013878189 + 9.5

Combine like terms: -9.013878189 + 9.5 = 0.486121811
g = 0.486121811

Simplifying
g = 0.486121811


Solution
The solution to the problem is based on the solutions
from the subproblems.
g = {18.513878189, 0.486121811}

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