3j^2+3j-2=0

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Solution for 3j^2+3j-2=0 equation:


Simplifying
3j2 + 3j + -2 = 0

Reorder the terms:
-2 + 3j + 3j2 = 0

Solving
-2 + 3j + 3j2 = 0

Solving for variable 'j'.

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
-0.6666666667 + j + j2 = 0

Move the constant term to the right:

Add '0.6666666667' to each side of the equation.
-0.6666666667 + j + 0.6666666667 + j2 = 0 + 0.6666666667

Reorder the terms:
-0.6666666667 + 0.6666666667 + j + j2 = 0 + 0.6666666667

Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000
0.0000000000 + j + j2 = 0 + 0.6666666667
j + j2 = 0 + 0.6666666667

Combine like terms: 0 + 0.6666666667 = 0.6666666667
j + j2 = 0.6666666667

The j term is j.  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.
 + 0.25 + j2 = 0.6666666667 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + j2 = 0.6666666667 + 0.25

Combine like terms: 0.6666666667 + 0.25 = 0.9166666667
1.25 + j2 = 0.9166666667

Factor a perfect square on the left side:
(j + 0.5)(j + 0.5) = 0.9166666667

Calculate the square root of the right side: 0.957427108

Break this problem into two subproblems by setting 
(j + 0.5) equal to 0.957427108 and -0.957427108.

Subproblem 1

j + 0.5 = 0.957427108 Simplifying j + 0.5 = 0.957427108 Reorder the terms: 0.5 + j = 0.957427108 Solving 0.5 + j = 0.957427108 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + j = 0.957427108 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + j = 0.957427108 + -0.5 j = 0.957427108 + -0.5 Combine like terms: 0.957427108 + -0.5 = 0.457427108 j = 0.457427108 Simplifying j = 0.457427108

Subproblem 2

j + 0.5 = -0.957427108 Simplifying j + 0.5 = -0.957427108 Reorder the terms: 0.5 + j = -0.957427108 Solving 0.5 + j = -0.957427108 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + j = -0.957427108 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + j = -0.957427108 + -0.5 j = -0.957427108 + -0.5 Combine like terms: -0.957427108 + -0.5 = -1.457427108 j = -1.457427108 Simplifying j = -1.457427108

Solution

The solution to the problem is based on the solutions from the subproblems. j = {0.457427108, -1.457427108}

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