d^2-4d-330=0

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Solution for d^2-4d-330=0 equation: 


Simplifying
d2 + -4d + -330 = 0

Reorder the terms:
-330 + -4d + d2 = 0

Solving
-330 + -4d + d2 = 0

Solving for variable 'd'.

Begin completing the square.

Move the constant term to the right:

Add '330' to each side of the equation.
-330 + -4d + 330 + d2 = 0 + 330

Reorder the terms:
-330 + 330 + -4d + d2 = 0 + 330

Combine like terms: -330 + 330 = 0
0 + -4d + d2 = 0 + 330
-4d + d2 = 0 + 330

Combine like terms: 0 + 330 = 330
-4d + d2 = 330

The d term is -4d.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4d + 4 + d2 = 330 + 4

Reorder the terms:
4 + -4d + d2 = 330 + 4

Combine like terms: 330 + 4 = 334
4 + -4d + d2 = 334

Factor a perfect square on the left side:
(d + -2)(d + -2) = 334

Calculate the square root of the right side: 18.275666882

Break this problem into two subproblems by setting 
(d + -2) equal to 18.275666882 and -18.275666882.


Subproblem 1
d + -2 = 18.275666882

Simplifying
d + -2 = 18.275666882

Reorder the terms:
-2 + d = 18.275666882

Solving
-2 + d = 18.275666882

Solving for variable 'd'.

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

Add '2' to each side of the equation.
-2 + 2 + d = 18.275666882 + 2

Combine like terms: -2 + 2 = 0
0 + d = 18.275666882 + 2
d = 18.275666882 + 2

Combine like terms: 18.275666882 + 2 = 20.275666882
d = 20.275666882

Simplifying
d = 20.275666882


Subproblem 2
d + -2 = -18.275666882

Simplifying
d + -2 = -18.275666882

Reorder the terms:
-2 + d = -18.275666882

Solving
-2 + d = -18.275666882

Solving for variable 'd'.

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

Add '2' to each side of the equation.
-2 + 2 + d = -18.275666882 + 2

Combine like terms: -2 + 2 = 0
0 + d = -18.275666882 + 2
d = -18.275666882 + 2

Combine like terms: -18.275666882 + 2 = -16.275666882
d = -16.275666882

Simplifying
d = -16.275666882


Solution
The solution to the problem is based on the solutions
from the subproblems.
d = {20.275666882, -16.275666882}

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