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Simplifying j2 + -12j + 1 = 0 Reorder the terms: 1 + -12j + j2 = 0 Solving 1 + -12j + j2 = 0 Solving for variable 'j'. Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + -12j + -1 + j2 = 0 + -1 Reorder the terms: 1 + -1 + -12j + j2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -12j + j2 = 0 + -1 -12j + j2 = 0 + -1 Combine like terms: 0 + -1 = -1 -12j + j2 = -1 The j term is -12j. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12j + 36 + j2 = -1 + 36 Reorder the terms: 36 + -12j + j2 = -1 + 36 Combine like terms: -1 + 36 = 35 36 + -12j + j2 = 35 Factor a perfect square on the left side: (j + -6)(j + -6) = 35 Calculate the square root of the right side: 5.916079783 Break this problem into two subproblems by setting (j + -6) equal to 5.916079783 and -5.916079783.Subproblem 1
j + -6 = 5.916079783 Simplifying j + -6 = 5.916079783 Reorder the terms: -6 + j = 5.916079783 Solving -6 + j = 5.916079783 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + j = 5.916079783 + 6 Combine like terms: -6 + 6 = 0 0 + j = 5.916079783 + 6 j = 5.916079783 + 6 Combine like terms: 5.916079783 + 6 = 11.916079783 j = 11.916079783 Simplifying j = 11.916079783Subproblem 2
j + -6 = -5.916079783 Simplifying j + -6 = -5.916079783 Reorder the terms: -6 + j = -5.916079783 Solving -6 + j = -5.916079783 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + j = -5.916079783 + 6 Combine like terms: -6 + 6 = 0 0 + j = -5.916079783 + 6 j = -5.916079783 + 6 Combine like terms: -5.916079783 + 6 = 0.083920217 j = 0.083920217 Simplifying j = 0.083920217Solution
The solution to the problem is based on the solutions from the subproblems. j = {11.916079783, 0.083920217}
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