g^2+22g+35=0

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Solution for g^2+22g+35=0 equation: 


Simplifying
g2 + 22g + 35 = 0

Reorder the terms:
35 + 22g + g2 = 0

Solving
35 + 22g + g2 = 0

Solving for variable 'g'.

Begin completing the square.

Move the constant term to the right:

Add '-35' to each side of the equation.
35 + 22g + -35 + g2 = 0 + -35

Reorder the terms:
35 + -35 + 22g + g2 = 0 + -35

Combine like terms: 35 + -35 = 0
0 + 22g + g2 = 0 + -35
22g + g2 = 0 + -35

Combine like terms: 0 + -35 = -35
22g + g2 = -35

The g term is 22g.  Take half its coefficient (11).
Square it (121) and add it to both sides.

Add '121' to each side of the equation.
22g + 121 + g2 = -35 + 121

Reorder the terms:
121 + 22g + g2 = -35 + 121

Combine like terms: -35 + 121 = 86
121 + 22g + g2 = 86

Factor a perfect square on the left side:
(g + 11)(g + 11) = 86

Calculate the square root of the right side: 9.273618495

Break this problem into two subproblems by setting 
(g + 11) equal to 9.273618495 and -9.273618495.


Subproblem 1
g + 11 = 9.273618495

Simplifying
g + 11 = 9.273618495

Reorder the terms:
11 + g = 9.273618495

Solving
11 + g = 9.273618495

Solving for variable 'g'.

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

Add '-11' to each side of the equation.
11 + -11 + g = 9.273618495 + -11

Combine like terms: 11 + -11 = 0
0 + g = 9.273618495 + -11
g = 9.273618495 + -11

Combine like terms: 9.273618495 + -11 = -1.726381505
g = -1.726381505

Simplifying
g = -1.726381505


Subproblem 2
g + 11 = -9.273618495

Simplifying
g + 11 = -9.273618495

Reorder the terms:
11 + g = -9.273618495

Solving
11 + g = -9.273618495

Solving for variable 'g'.

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

Add '-11' to each side of the equation.
11 + -11 + g = -9.273618495 + -11

Combine like terms: 11 + -11 = 0
0 + g = -9.273618495 + -11
g = -9.273618495 + -11

Combine like terms: -9.273618495 + -11 = -20.273618495
g = -20.273618495

Simplifying
g = -20.273618495


Solution
The solution to the problem is based on the solutions
from the subproblems.
g = {-1.726381505, -20.273618495}

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