3d^2+54d-33=0

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Solution for 3d^2+54d-33=0 equation: 


Simplifying
3d2 + 54d + -33 = 0

Reorder the terms:
-33 + 54d + 3d2 = 0

Solving
-33 + 54d + 3d2 = 0

Solving for variable 'd'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-11 + 18d + d2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-11 + 18d + d2)' equal to zero and attempt to solve:

Simplifying
-11 + 18d + d2 = 0

Solving
-11 + 18d + d2 = 0

Begin completing the square.

Move the constant term to the right:

Add '11' to each side of the equation.
-11 + 18d + 11 + d2 = 0 + 11

Reorder the terms:
-11 + 11 + 18d + d2 = 0 + 11

Combine like terms: -11 + 11 = 0
0 + 18d + d2 = 0 + 11
18d + d2 = 0 + 11

Combine like terms: 0 + 11 = 11
18d + d2 = 11

The d term is 18d.  Take half its coefficient (9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
18d + 81 + d2 = 11 + 81

Reorder the terms:
81 + 18d + d2 = 11 + 81

Combine like terms: 11 + 81 = 92
81 + 18d + d2 = 92

Factor a perfect square on the left side:
(d + 9)(d + 9) = 92

Calculate the square root of the right side: 9.591663047

Break this problem into two subproblems by setting 
(d + 9) equal to 9.591663047 and -9.591663047.


Subproblem 1
d + 9 = 9.591663047

Simplifying
d + 9 = 9.591663047

Reorder the terms:
9 + d = 9.591663047

Solving
9 + d = 9.591663047

Solving for variable 'd'.

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

Add '-9' to each side of the equation.
9 + -9 + d = 9.591663047 + -9

Combine like terms: 9 + -9 = 0
0 + d = 9.591663047 + -9
d = 9.591663047 + -9

Combine like terms: 9.591663047 + -9 = 0.591663047
d = 0.591663047

Simplifying
d = 0.591663047


Subproblem 2
d + 9 = -9.591663047

Simplifying
d + 9 = -9.591663047

Reorder the terms:
9 + d = -9.591663047

Solving
9 + d = -9.591663047

Solving for variable 'd'.

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

Add '-9' to each side of the equation.
9 + -9 + d = -9.591663047 + -9

Combine like terms: 9 + -9 = 0
0 + d = -9.591663047 + -9
d = -9.591663047 + -9

Combine like terms: -9.591663047 + -9 = -18.591663047
d = -18.591663047

Simplifying
d = -18.591663047


Solution
The solution to the problem is based on the solutions
from the subproblems.
d = {0.591663047, -18.591663047}
Solution
d = {0.591663047, -18.591663047}

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