3j^2-6j=141

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Solution for 3j^2-6j=141 equation:


Simplifying
3j2 + -6j = 141

Reorder the terms:
-6j + 3j2 = 141

Solving
-6j + 3j2 = 141

Solving for variable 'j'.

Reorder the terms:
-141 + -6j + 3j2 = 141 + -141

Combine like terms: 141 + -141 = 0
-141 + -6j + 3j2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-47 + -2j + j2) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(-47 + -2j + j2)' equal to zero and attempt to solve: Simplifying -47 + -2j + j2 = 0 Solving -47 + -2j + j2 = 0 Begin completing the square. Move the constant term to the right: Add '47' to each side of the equation. -47 + -2j + 47 + j2 = 0 + 47 Reorder the terms: -47 + 47 + -2j + j2 = 0 + 47 Combine like terms: -47 + 47 = 0 0 + -2j + j2 = 0 + 47 -2j + j2 = 0 + 47 Combine like terms: 0 + 47 = 47 -2j + j2 = 47 The j term is -2j. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2j + 1 + j2 = 47 + 1 Reorder the terms: 1 + -2j + j2 = 47 + 1 Combine like terms: 47 + 1 = 48 1 + -2j + j2 = 48 Factor a perfect square on the left side: (j + -1)(j + -1) = 48 Calculate the square root of the right side: 6.92820323 Break this problem into two subproblems by setting (j + -1) equal to 6.92820323 and -6.92820323.

Subproblem 1

j + -1 = 6.92820323 Simplifying j + -1 = 6.92820323 Reorder the terms: -1 + j = 6.92820323 Solving -1 + j = 6.92820323 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + j = 6.92820323 + 1 Combine like terms: -1 + 1 = 0 0 + j = 6.92820323 + 1 j = 6.92820323 + 1 Combine like terms: 6.92820323 + 1 = 7.92820323 j = 7.92820323 Simplifying j = 7.92820323

Subproblem 2

j + -1 = -6.92820323 Simplifying j + -1 = -6.92820323 Reorder the terms: -1 + j = -6.92820323 Solving -1 + j = -6.92820323 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + j = -6.92820323 + 1 Combine like terms: -1 + 1 = 0 0 + j = -6.92820323 + 1 j = -6.92820323 + 1 Combine like terms: -6.92820323 + 1 = -5.92820323 j = -5.92820323 Simplifying j = -5.92820323

Solution

The solution to the problem is based on the solutions from the subproblems. j = {7.92820323, -5.92820323}

Solution

j = {7.92820323, -5.92820323}

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