3d^2+40d+9=0

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Solution for 3d^2+40d+9=0 equation: 


Simplifying
3d2 + 40d + 9 = 0

Reorder the terms:
9 + 40d + 3d2 = 0

Solving
9 + 40d + 3d2 = 0

Solving for variable 'd'.

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
3 + 13.33333333d + d2 = 0

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + 13.33333333d + -3 + d2 = 0 + -3

Reorder the terms:
3 + -3 + 13.33333333d + d2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 13.33333333d + d2 = 0 + -3
13.33333333d + d2 = 0 + -3

Combine like terms: 0 + -3 = -3
13.33333333d + d2 = -3

The d term is 13.33333333d.  Take half its coefficient (6.666666665).
Square it (44.44444442) and add it to both sides.

Add '44.44444442' to each side of the equation.
13.33333333d + 44.44444442 + d2 = -3 + 44.44444442

Reorder the terms:
44.44444442 + 13.33333333d + d2 = -3 + 44.44444442

Combine like terms: -3 + 44.44444442 = 41.44444442
44.44444442 + 13.33333333d + d2 = 41.44444442

Factor a perfect square on the left side:
(d + 6.666666665)(d + 6.666666665) = 41.44444442

Calculate the square root of the right side: 6.43773597

Break this problem into two subproblems by setting 
(d + 6.666666665) equal to 6.43773597 and -6.43773597.


Subproblem 1
d + 6.666666665 = 6.43773597

Simplifying
d + 6.666666665 = 6.43773597

Reorder the terms:
6.666666665 + d = 6.43773597

Solving
6.666666665 + d = 6.43773597

Solving for variable 'd'.

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

Add '-6.666666665' to each side of the equation.
6.666666665 + -6.666666665 + d = 6.43773597 + -6.666666665

Combine like terms: 6.666666665 + -6.666666665 = 0.000000000
0.000000000 + d = 6.43773597 + -6.666666665
d = 6.43773597 + -6.666666665

Combine like terms: 6.43773597 + -6.666666665 = -0.228930695
d = -0.228930695

Simplifying
d = -0.228930695


Subproblem 2
d + 6.666666665 = -6.43773597

Simplifying
d + 6.666666665 = -6.43773597

Reorder the terms:
6.666666665 + d = -6.43773597

Solving
6.666666665 + d = -6.43773597

Solving for variable 'd'.

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

Add '-6.666666665' to each side of the equation.
6.666666665 + -6.666666665 + d = -6.43773597 + -6.666666665

Combine like terms: 6.666666665 + -6.666666665 = 0.000000000
0.000000000 + d = -6.43773597 + -6.666666665
d = -6.43773597 + -6.666666665

Combine like terms: -6.43773597 + -6.666666665 = -13.104402635
d = -13.104402635

Simplifying
d = -13.104402635


Solution
The solution to the problem is based on the solutions
from the subproblems.
d = {-0.228930695, -13.104402635}

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