g^2+11g-468=0

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Solution for g^2+11g-468=0 equation: 


Simplifying
g2 + 11g + -468 = 0

Reorder the terms:
-468 + 11g + g2 = 0

Solving
-468 + 11g + g2 = 0

Solving for variable 'g'.

Begin completing the square.

Move the constant term to the right:

Add '468' to each side of the equation.
-468 + 11g + 468 + g2 = 0 + 468

Reorder the terms:
-468 + 468 + 11g + g2 = 0 + 468

Combine like terms: -468 + 468 = 0
0 + 11g + g2 = 0 + 468
11g + g2 = 0 + 468

Combine like terms: 0 + 468 = 468
11g + g2 = 468

The g term is 11g.  Take half its coefficient (5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
11g + 30.25 + g2 = 468 + 30.25

Reorder the terms:
30.25 + 11g + g2 = 468 + 30.25

Combine like terms: 468 + 30.25 = 498.25
30.25 + 11g + g2 = 498.25

Factor a perfect square on the left side:
(g + 5.5)(g + 5.5) = 498.25

Calculate the square root of the right side: 22.321514286

Break this problem into two subproblems by setting 
(g + 5.5) equal to 22.321514286 and -22.321514286.


Subproblem 1
g + 5.5 = 22.321514286

Simplifying
g + 5.5 = 22.321514286

Reorder the terms:
5.5 + g = 22.321514286

Solving
5.5 + g = 22.321514286

Solving for variable 'g'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + g = 22.321514286 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + g = 22.321514286 + -5.5
g = 22.321514286 + -5.5

Combine like terms: 22.321514286 + -5.5 = 16.821514286
g = 16.821514286

Simplifying
g = 16.821514286


Subproblem 2
g + 5.5 = -22.321514286

Simplifying
g + 5.5 = -22.321514286

Reorder the terms:
5.5 + g = -22.321514286

Solving
5.5 + g = -22.321514286

Solving for variable 'g'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + g = -22.321514286 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + g = -22.321514286 + -5.5
g = -22.321514286 + -5.5

Combine like terms: -22.321514286 + -5.5 = -27.821514286
g = -27.821514286

Simplifying
g = -27.821514286


Solution
The solution to the problem is based on the solutions
from the subproblems.
g = {16.821514286, -27.821514286}

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