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Simplifying -2j2 + -32j = -62 Reorder the terms: -32j + -2j2 = -62 Solving -32j + -2j2 = -62 Solving for variable 'j'. Reorder the terms: 62 + -32j + -2j2 = -62 + 62 Combine like terms: -62 + 62 = 0 62 + -32j + -2j2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(31 + -16j + -1j2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(31 + -16j + -1j2)' equal to zero and attempt to solve: Simplifying 31 + -16j + -1j2 = 0 Solving 31 + -16j + -1j2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -31 + 16j + j2 = 0 Move the constant term to the right: Add '31' to each side of the equation. -31 + 16j + 31 + j2 = 0 + 31 Reorder the terms: -31 + 31 + 16j + j2 = 0 + 31 Combine like terms: -31 + 31 = 0 0 + 16j + j2 = 0 + 31 16j + j2 = 0 + 31 Combine like terms: 0 + 31 = 31 16j + j2 = 31 The j term is 16j. Take half its coefficient (8). Square it (64) and add it to both sides. Add '64' to each side of the equation. 16j + 64 + j2 = 31 + 64 Reorder the terms: 64 + 16j + j2 = 31 + 64 Combine like terms: 31 + 64 = 95 64 + 16j + j2 = 95 Factor a perfect square on the left side: (j + 8)(j + 8) = 95 Calculate the square root of the right side: 9.746794345 Break this problem into two subproblems by setting (j + 8) equal to 9.746794345 and -9.746794345.Subproblem 1
j + 8 = 9.746794345 Simplifying j + 8 = 9.746794345 Reorder the terms: 8 + j = 9.746794345 Solving 8 + j = 9.746794345 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + j = 9.746794345 + -8 Combine like terms: 8 + -8 = 0 0 + j = 9.746794345 + -8 j = 9.746794345 + -8 Combine like terms: 9.746794345 + -8 = 1.746794345 j = 1.746794345 Simplifying j = 1.746794345Subproblem 2
j + 8 = -9.746794345 Simplifying j + 8 = -9.746794345 Reorder the terms: 8 + j = -9.746794345 Solving 8 + j = -9.746794345 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + j = -9.746794345 + -8 Combine like terms: 8 + -8 = 0 0 + j = -9.746794345 + -8 j = -9.746794345 + -8 Combine like terms: -9.746794345 + -8 = -17.746794345 j = -17.746794345 Simplifying j = -17.746794345Solution
The solution to the problem is based on the solutions from the subproblems. j = {1.746794345, -17.746794345}Solution
j = {1.746794345, -17.746794345}
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