3j^2-9j-3=0

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Solution for 3j^2-9j-3=0 equation:


Simplifying
3j2 + -9j + -3 = 0

Reorder the terms:
-3 + -9j + 3j2 = 0

Solving
-3 + -9j + 3j2 = 0

Solving for variable 'j'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-1 + -3j + j2) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(-1 + -3j + j2)' equal to zero and attempt to solve: Simplifying -1 + -3j + j2 = 0 Solving -1 + -3j + j2 = 0 Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + -3j + 1 + j2 = 0 + 1 Reorder the terms: -1 + 1 + -3j + j2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -3j + j2 = 0 + 1 -3j + j2 = 0 + 1 Combine like terms: 0 + 1 = 1 -3j + j2 = 1 The j term is -3j. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3j + 2.25 + j2 = 1 + 2.25 Reorder the terms: 2.25 + -3j + j2 = 1 + 2.25 Combine like terms: 1 + 2.25 = 3.25 2.25 + -3j + j2 = 3.25 Factor a perfect square on the left side: (j + -1.5)(j + -1.5) = 3.25 Calculate the square root of the right side: 1.802775638 Break this problem into two subproblems by setting (j + -1.5) equal to 1.802775638 and -1.802775638.

Subproblem 1

j + -1.5 = 1.802775638 Simplifying j + -1.5 = 1.802775638 Reorder the terms: -1.5 + j = 1.802775638 Solving -1.5 + j = 1.802775638 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + j = 1.802775638 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + j = 1.802775638 + 1.5 j = 1.802775638 + 1.5 Combine like terms: 1.802775638 + 1.5 = 3.302775638 j = 3.302775638 Simplifying j = 3.302775638

Subproblem 2

j + -1.5 = -1.802775638 Simplifying j + -1.5 = -1.802775638 Reorder the terms: -1.5 + j = -1.802775638 Solving -1.5 + j = -1.802775638 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + j = -1.802775638 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + j = -1.802775638 + 1.5 j = -1.802775638 + 1.5 Combine like terms: -1.802775638 + 1.5 = -0.302775638 j = -0.302775638 Simplifying j = -0.302775638

Solution

The solution to the problem is based on the solutions from the subproblems. j = {3.302775638, -0.302775638}

Solution

j = {3.302775638, -0.302775638}

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