2d^2-16d-323=0

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Solution for 2d^2-16d-323=0 equation: 


Simplifying
2d2 + -16d + -323 = 0

Reorder the terms:
-323 + -16d + 2d2 = 0

Solving
-323 + -16d + 2d2 = 0

Solving for variable 'd'.

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

Divide each side by '2'.
-161.5 + -8d + d2 = 0

Move the constant term to the right:

Add '161.5' to each side of the equation.
-161.5 + -8d + 161.5 + d2 = 0 + 161.5

Reorder the terms:
-161.5 + 161.5 + -8d + d2 = 0 + 161.5

Combine like terms: -161.5 + 161.5 = 0.0
0.0 + -8d + d2 = 0 + 161.5
-8d + d2 = 0 + 161.5

Combine like terms: 0 + 161.5 = 161.5
-8d + d2 = 161.5

The d term is -8d.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8d + 16 + d2 = 161.5 + 16

Reorder the terms:
16 + -8d + d2 = 161.5 + 16

Combine like terms: 161.5 + 16 = 177.5
16 + -8d + d2 = 177.5

Factor a perfect square on the left side:
(d + -4)(d + -4) = 177.5

Calculate the square root of the right side: 13.322912594

Break this problem into two subproblems by setting 
(d + -4) equal to 13.322912594 and -13.322912594.


Subproblem 1
d + -4 = 13.322912594

Simplifying
d + -4 = 13.322912594

Reorder the terms:
-4 + d = 13.322912594

Solving
-4 + d = 13.322912594

Solving for variable 'd'.

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

Add '4' to each side of the equation.
-4 + 4 + d = 13.322912594 + 4

Combine like terms: -4 + 4 = 0
0 + d = 13.322912594 + 4
d = 13.322912594 + 4

Combine like terms: 13.322912594 + 4 = 17.322912594
d = 17.322912594

Simplifying
d = 17.322912594


Subproblem 2
d + -4 = -13.322912594

Simplifying
d + -4 = -13.322912594

Reorder the terms:
-4 + d = -13.322912594

Solving
-4 + d = -13.322912594

Solving for variable 'd'.

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

Add '4' to each side of the equation.
-4 + 4 + d = -13.322912594 + 4

Combine like terms: -4 + 4 = 0
0 + d = -13.322912594 + 4
d = -13.322912594 + 4

Combine like terms: -13.322912594 + 4 = -9.322912594
d = -9.322912594

Simplifying
d = -9.322912594


Solution
The solution to the problem is based on the solutions
from the subproblems.
d = {17.322912594, -9.322912594}

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