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Simplifying 3j2 + 12j + -6 = 0 Reorder the terms: -6 + 12j + 3j2 = 0 Solving -6 + 12j + 3j2 = 0 Solving for variable 'j'. Factor out the Greatest Common Factor (GCF), '3'. 3(-2 + 4j + j2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-2 + 4j + j2)' equal to zero and attempt to solve: Simplifying -2 + 4j + j2 = 0 Solving -2 + 4j + j2 = 0 Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + 4j + 2 + j2 = 0 + 2 Reorder the terms: -2 + 2 + 4j + j2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 4j + j2 = 0 + 2 4j + j2 = 0 + 2 Combine like terms: 0 + 2 = 2 4j + j2 = 2 The j term is 4j. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4j + 4 + j2 = 2 + 4 Reorder the terms: 4 + 4j + j2 = 2 + 4 Combine like terms: 2 + 4 = 6 4 + 4j + j2 = 6 Factor a perfect square on the left side: (j + 2)(j + 2) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (j + 2) equal to 2.449489743 and -2.449489743.Subproblem 1
j + 2 = 2.449489743 Simplifying j + 2 = 2.449489743 Reorder the terms: 2 + j = 2.449489743 Solving 2 + j = 2.449489743 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + j = 2.449489743 + -2 Combine like terms: 2 + -2 = 0 0 + j = 2.449489743 + -2 j = 2.449489743 + -2 Combine like terms: 2.449489743 + -2 = 0.449489743 j = 0.449489743 Simplifying j = 0.449489743Subproblem 2
j + 2 = -2.449489743 Simplifying j + 2 = -2.449489743 Reorder the terms: 2 + j = -2.449489743 Solving 2 + j = -2.449489743 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + j = -2.449489743 + -2 Combine like terms: 2 + -2 = 0 0 + j = -2.449489743 + -2 j = -2.449489743 + -2 Combine like terms: -2.449489743 + -2 = -4.449489743 j = -4.449489743 Simplifying j = -4.449489743Solution
The solution to the problem is based on the solutions from the subproblems. j = {0.449489743, -4.449489743}Solution
j = {0.449489743, -4.449489743}
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