3d^2-3d-27=0

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Solution for 3d^2-3d-27=0 equation: 


Simplifying
3d2 + -3d + -27 = 0

Reorder the terms:
-27 + -3d + 3d2 = 0

Solving
-27 + -3d + 3d2 = 0

Solving for variable 'd'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-9 + -1d + d2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-9 + -1d + d2)' equal to zero and attempt to solve:

Simplifying
-9 + -1d + d2 = 0

Solving
-9 + -1d + d2 = 0

Begin completing the square.

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + -1d + 9 + d2 = 0 + 9

Reorder the terms:
-9 + 9 + -1d + d2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1d + d2 = 0 + 9
-1d + d2 = 0 + 9

Combine like terms: 0 + 9 = 9
-1d + d2 = 9

The d term is -1d.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1d + 0.25 + d2 = 9 + 0.25

Reorder the terms:
0.25 + -1d + d2 = 9 + 0.25

Combine like terms: 9 + 0.25 = 9.25
0.25 + -1d + d2 = 9.25

Factor a perfect square on the left side:
(d + -0.5)(d + -0.5) = 9.25

Calculate the square root of the right side: 3.041381265

Break this problem into two subproblems by setting 
(d + -0.5) equal to 3.041381265 and -3.041381265.


Subproblem 1
d + -0.5 = 3.041381265

Simplifying
d + -0.5 = 3.041381265

Reorder the terms:
-0.5 + d = 3.041381265

Solving
-0.5 + d = 3.041381265

Solving for variable 'd'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + d = 3.041381265 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + d = 3.041381265 + 0.5
d = 3.041381265 + 0.5

Combine like terms: 3.041381265 + 0.5 = 3.541381265
d = 3.541381265

Simplifying
d = 3.541381265


Subproblem 2
d + -0.5 = -3.041381265

Simplifying
d + -0.5 = -3.041381265

Reorder the terms:
-0.5 + d = -3.041381265

Solving
-0.5 + d = -3.041381265

Solving for variable 'd'.

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

Add '0.5' to each side of the equation.
-0.5 + 0.5 + d = -3.041381265 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + d = -3.041381265 + 0.5
d = -3.041381265 + 0.5

Combine like terms: -3.041381265 + 0.5 = -2.541381265
d = -2.541381265

Simplifying
d = -2.541381265


Solution
The solution to the problem is based on the solutions
from the subproblems.
d = {3.541381265, -2.541381265}
Solution
d = {3.541381265, -2.541381265}

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