3j^2-30j-93=0

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Solution for 3j^2-30j-93=0 equation:


Simplifying
3j2 + -30j + -93 = 0

Reorder the terms:
-93 + -30j + 3j2 = 0

Solving
-93 + -30j + 3j2 = 0

Solving for variable 'j'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-31 + -10j + j2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-31 + -10j + j2)' equal to zero and attempt to solve:

Simplifying
-31 + -10j + j2 = 0

Solving
-31 + -10j + j2 = 0

Begin completing the square.

Move the constant term to the right:

Add '31' to each side of the equation.
-31 + -10j + 31 + j2 = 0 + 31

Reorder the terms:
-31 + 31 + -10j + j2 = 0 + 31

Combine like terms: -31 + 31 = 0
0 + -10j + j2 = 0 + 31
-10j + j2 = 0 + 31

Combine like terms: 0 + 31 = 31
-10j + j2 = 31

The j term is -10j.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10j + 25 + j2 = 31 + 25

Reorder the terms:
25 + -10j + j2 = 31 + 25

Combine like terms: 31 + 25 = 56
25 + -10j + j2 = 56

Factor a perfect square on the left side:
(j + -5)(j + -5) = 56

Calculate the square root of the right side: 7.483314774

Break this problem into two subproblems by setting 
(j + -5) equal to 7.483314774 and -7.483314774.


Subproblem 1
j + -5 = 7.483314774

Simplifying
j + -5 = 7.483314774

Reorder the terms:
-5 + j = 7.483314774

Solving
-5 + j = 7.483314774

Solving for variable 'j'.

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

Add '5' to each side of the equation.
-5 + 5 + j = 7.483314774 + 5

Combine like terms: -5 + 5 = 0
0 + j = 7.483314774 + 5
j = 7.483314774 + 5

Combine like terms: 7.483314774 + 5 = 12.483314774
j = 12.483314774

Simplifying
j = 12.483314774


Subproblem 2
j + -5 = -7.483314774

Simplifying
j + -5 = -7.483314774

Reorder the terms:
-5 + j = -7.483314774

Solving
-5 + j = -7.483314774

Solving for variable 'j'.

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

Add '5' to each side of the equation.
-5 + 5 + j = -7.483314774 + 5

Combine like terms: -5 + 5 = 0
0 + j = -7.483314774 + 5
j = -7.483314774 + 5

Combine like terms: -7.483314774 + 5 = -2.483314774
j = -2.483314774

Simplifying
j = -2.483314774


Solution
The solution to the problem is based on the solutions
from the subproblems.
j = {12.483314774, -2.483314774}
Solution
j = {12.483314774, -2.483314774}

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