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Simplifying -2j2 + -8j + 6 = 0 Reorder the terms: 6 + -8j + -2j2 = 0 Solving 6 + -8j + -2j2 = 0 Solving for variable 'j'. Factor out the Greatest Common Factor (GCF), '2'. 2(3 + -4j + -1j2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + -4j + -1j2)' equal to zero and attempt to solve: Simplifying 3 + -4j + -1j2 = 0 Solving 3 + -4j + -1j2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -3 + 4j + j2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 4j + 3 + j2 = 0 + 3 Reorder the terms: -3 + 3 + 4j + j2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 4j + j2 = 0 + 3 4j + j2 = 0 + 3 Combine like terms: 0 + 3 = 3 4j + j2 = 3 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 = 3 + 4 Reorder the terms: 4 + 4j + j2 = 3 + 4 Combine like terms: 3 + 4 = 7 4 + 4j + j2 = 7 Factor a perfect square on the left side: (j + 2)(j + 2) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (j + 2) equal to 2.645751311 and -2.645751311.Subproblem 1
j + 2 = 2.645751311 Simplifying j + 2 = 2.645751311 Reorder the terms: 2 + j = 2.645751311 Solving 2 + j = 2.645751311 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 = 2.645751311 + -2 Combine like terms: 2 + -2 = 0 0 + j = 2.645751311 + -2 j = 2.645751311 + -2 Combine like terms: 2.645751311 + -2 = 0.645751311 j = 0.645751311 Simplifying j = 0.645751311Subproblem 2
j + 2 = -2.645751311 Simplifying j + 2 = -2.645751311 Reorder the terms: 2 + j = -2.645751311 Solving 2 + j = -2.645751311 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 = -2.645751311 + -2 Combine like terms: 2 + -2 = 0 0 + j = -2.645751311 + -2 j = -2.645751311 + -2 Combine like terms: -2.645751311 + -2 = -4.645751311 j = -4.645751311 Simplifying j = -4.645751311Solution
The solution to the problem is based on the solutions from the subproblems. j = {0.645751311, -4.645751311}Solution
j = {0.645751311, -4.645751311}
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