3j^2+66j+21=0

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Solution for 3j^2+66j+21=0 equation: 


Simplifying
3j2 + 66j + 21 = 0

Reorder the terms:
21 + 66j + 3j2 = 0

Solving
21 + 66j + 3j2 = 0

Solving for variable 'j'.

Factor out the Greatest Common Factor (GCF), '3'.
3(7 + 22j + j2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(7 + 22j + j2)' equal to zero and attempt to solve:

Simplifying
7 + 22j + j2 = 0

Solving
7 + 22j + j2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-7' to each side of the equation.
7 + 22j + -7 + j2 = 0 + -7

Reorder the terms:
7 + -7 + 22j + j2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 22j + j2 = 0 + -7
22j + j2 = 0 + -7

Combine like terms: 0 + -7 = -7
22j + j2 = -7

The j term is 22j.  Take half its coefficient (11).
Square it (121) and add it to both sides.

Add '121' to each side of the equation.
22j + 121 + j2 = -7 + 121

Reorder the terms:
121 + 22j + j2 = -7 + 121

Combine like terms: -7 + 121 = 114
121 + 22j + j2 = 114

Factor a perfect square on the left side:
(j + 11)(j + 11) = 114

Calculate the square root of the right side: 10.677078252

Break this problem into two subproblems by setting 
(j + 11) equal to 10.677078252 and -10.677078252.


Subproblem 1
j + 11 = 10.677078252

Simplifying
j + 11 = 10.677078252

Reorder the terms:
11 + j = 10.677078252

Solving
11 + j = 10.677078252

Solving for variable 'j'.

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

Add '-11' to each side of the equation.
11 + -11 + j = 10.677078252 + -11

Combine like terms: 11 + -11 = 0
0 + j = 10.677078252 + -11
j = 10.677078252 + -11

Combine like terms: 10.677078252 + -11 = -0.322921748
j = -0.322921748

Simplifying
j = -0.322921748


Subproblem 2
j + 11 = -10.677078252

Simplifying
j + 11 = -10.677078252

Reorder the terms:
11 + j = -10.677078252

Solving
11 + j = -10.677078252

Solving for variable 'j'.

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

Add '-11' to each side of the equation.
11 + -11 + j = -10.677078252 + -11

Combine like terms: 11 + -11 = 0
0 + j = -10.677078252 + -11
j = -10.677078252 + -11

Combine like terms: -10.677078252 + -11 = -21.677078252
j = -21.677078252

Simplifying
j = -21.677078252


Solution
The solution to the problem is based on the solutions
from the subproblems.
j = {-0.322921748, -21.677078252}
Solution
j = {-0.322921748, -21.677078252}

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