d^2-33d-180=0

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Solution for d^2-33d-180=0 equation: 


Simplifying
d2 + -33d + -180 = 0

Reorder the terms:
-180 + -33d + d2 = 0

Solving
-180 + -33d + d2 = 0

Solving for variable 'd'.

Begin completing the square.

Move the constant term to the right:

Add '180' to each side of the equation.
-180 + -33d + 180 + d2 = 0 + 180

Reorder the terms:
-180 + 180 + -33d + d2 = 0 + 180

Combine like terms: -180 + 180 = 0
0 + -33d + d2 = 0 + 180
-33d + d2 = 0 + 180

Combine like terms: 0 + 180 = 180
-33d + d2 = 180

The d term is -33d.  Take half its coefficient (-16.5).
Square it (272.25) and add it to both sides.

Add '272.25' to each side of the equation.
-33d + 272.25 + d2 = 180 + 272.25

Reorder the terms:
272.25 + -33d + d2 = 180 + 272.25

Combine like terms: 180 + 272.25 = 452.25
272.25 + -33d + d2 = 452.25

Factor a perfect square on the left side:
(d + -16.5)(d + -16.5) = 452.25

Calculate the square root of the right side: 21.266170318

Break this problem into two subproblems by setting 
(d + -16.5) equal to 21.266170318 and -21.266170318.


Subproblem 1
d + -16.5 = 21.266170318

Simplifying
d + -16.5 = 21.266170318

Reorder the terms:
-16.5 + d = 21.266170318

Solving
-16.5 + d = 21.266170318

Solving for variable 'd'.

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

Add '16.5' to each side of the equation.
-16.5 + 16.5 + d = 21.266170318 + 16.5

Combine like terms: -16.5 + 16.5 = 0.0
0.0 + d = 21.266170318 + 16.5
d = 21.266170318 + 16.5

Combine like terms: 21.266170318 + 16.5 = 37.766170318
d = 37.766170318

Simplifying
d = 37.766170318


Subproblem 2
d + -16.5 = -21.266170318

Simplifying
d + -16.5 = -21.266170318

Reorder the terms:
-16.5 + d = -21.266170318

Solving
-16.5 + d = -21.266170318

Solving for variable 'd'.

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

Add '16.5' to each side of the equation.
-16.5 + 16.5 + d = -21.266170318 + 16.5

Combine like terms: -16.5 + 16.5 = 0.0
0.0 + d = -21.266170318 + 16.5
d = -21.266170318 + 16.5

Combine like terms: -21.266170318 + 16.5 = -4.766170318
d = -4.766170318

Simplifying
d = -4.766170318


Solution
The solution to the problem is based on the solutions
from the subproblems.
d = {37.766170318, -4.766170318}

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