g(12+g)-9g-17=

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Solution for g(12+g)-9g-17= equation: 


Simplifying
g(12 + g) + -9g + -17 = 0
(12 * g + g * g) + -9g + -17 = 0
(12g + g2) + -9g + -17 = 0

Reorder the terms:
-17 + 12g + -9g + g2 = 0

Combine like terms: 12g + -9g = 3g
-17 + 3g + g2 = 0

Solving
-17 + 3g + 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 + 3g + 17 + g2 = 0 + 17

Reorder the terms:
-17 + 17 + 3g + g2 = 0 + 17

Combine like terms: -17 + 17 = 0
0 + 3g + g2 = 0 + 17
3g + g2 = 0 + 17

Combine like terms: 0 + 17 = 17
3g + g2 = 17

The g term is 3g.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3g + 2.25 + g2 = 17 + 2.25

Reorder the terms:
2.25 + 3g + g2 = 17 + 2.25

Combine like terms: 17 + 2.25 = 19.25
2.25 + 3g + g2 = 19.25

Factor a perfect square on the left side:
(g + 1.5)(g + 1.5) = 19.25

Calculate the square root of the right side: 4.387482194

Break this problem into two subproblems by setting 
(g + 1.5) equal to 4.387482194 and -4.387482194.


Subproblem 1
g + 1.5 = 4.387482194

Simplifying
g + 1.5 = 4.387482194

Reorder the terms:
1.5 + g = 4.387482194

Solving
1.5 + g = 4.387482194

Solving for variable 'g'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + g = 4.387482194 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + g = 4.387482194 + -1.5
g = 4.387482194 + -1.5

Combine like terms: 4.387482194 + -1.5 = 2.887482194
g = 2.887482194

Simplifying
g = 2.887482194


Subproblem 2
g + 1.5 = -4.387482194

Simplifying
g + 1.5 = -4.387482194

Reorder the terms:
1.5 + g = -4.387482194

Solving
1.5 + g = -4.387482194

Solving for variable 'g'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + g = -4.387482194 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + g = -4.387482194 + -1.5
g = -4.387482194 + -1.5

Combine like terms: -4.387482194 + -1.5 = -5.887482194
g = -5.887482194

Simplifying
g = -5.887482194


Solution
The solution to the problem is based on the solutions
from the subproblems.
g = {2.887482194, -5.887482194}

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