10*d*d+137d+30=0

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Solution for 10*d*d+137d+30=0 equation: 


Simplifying
10d * d + 137d + 30 = 0

Multiply d * d
10d2 + 137d + 30 = 0

Reorder the terms:
30 + 137d + 10d2 = 0

Solving
30 + 137d + 10d2 = 0

Solving for variable 'd'.

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

Divide each side by '10'.
3 + 13.7d + d2 = 0

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + 13.7d + -3 + d2 = 0 + -3

Reorder the terms:
3 + -3 + 13.7d + d2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 13.7d + d2 = 0 + -3
13.7d + d2 = 0 + -3

Combine like terms: 0 + -3 = -3
13.7d + d2 = -3

The d term is 13.7d.  Take half its coefficient (6.85).
Square it (46.9225) and add it to both sides.

Add '46.9225' to each side of the equation.
13.7d + 46.9225 + d2 = -3 + 46.9225

Reorder the terms:
46.9225 + 13.7d + d2 = -3 + 46.9225

Combine like terms: -3 + 46.9225 = 43.9225
46.9225 + 13.7d + d2 = 43.9225

Factor a perfect square on the left side:
(d + 6.85)(d + 6.85) = 43.9225

Calculate the square root of the right side: 6.627405224

Break this problem into two subproblems by setting 
(d + 6.85) equal to 6.627405224 and -6.627405224.


Subproblem 1
d + 6.85 = 6.627405224

Simplifying
d + 6.85 = 6.627405224

Reorder the terms:
6.85 + d = 6.627405224

Solving
6.85 + d = 6.627405224

Solving for variable 'd'.

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

Add '-6.85' to each side of the equation.
6.85 + -6.85 + d = 6.627405224 + -6.85

Combine like terms: 6.85 + -6.85 = 0.00
0.00 + d = 6.627405224 + -6.85
d = 6.627405224 + -6.85

Combine like terms: 6.627405224 + -6.85 = -0.222594776
d = -0.222594776

Simplifying
d = -0.222594776


Subproblem 2
d + 6.85 = -6.627405224

Simplifying
d + 6.85 = -6.627405224

Reorder the terms:
6.85 + d = -6.627405224

Solving
6.85 + d = -6.627405224

Solving for variable 'd'.

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

Add '-6.85' to each side of the equation.
6.85 + -6.85 + d = -6.627405224 + -6.85

Combine like terms: 6.85 + -6.85 = 0.00
0.00 + d = -6.627405224 + -6.85
d = -6.627405224 + -6.85

Combine like terms: -6.627405224 + -6.85 = -13.477405224
d = -13.477405224

Simplifying
d = -13.477405224


Solution
The solution to the problem is based on the solutions
from the subproblems.
d = {-0.222594776, -13.477405224}

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