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Simplifying j2 + -8j + 6 = 0 Reorder the terms: 6 + -8j + j2 = 0 Solving 6 + -8j + j2 = 0 Solving for variable 'j'. Begin completing the square. Move the constant term to the right: Add '-6' to each side of the equation. 6 + -8j + -6 + j2 = 0 + -6 Reorder the terms: 6 + -6 + -8j + j2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -8j + j2 = 0 + -6 -8j + j2 = 0 + -6 Combine like terms: 0 + -6 = -6 -8j + j2 = -6 The j term is -8j. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8j + 16 + j2 = -6 + 16 Reorder the terms: 16 + -8j + j2 = -6 + 16 Combine like terms: -6 + 16 = 10 16 + -8j + j2 = 10 Factor a perfect square on the left side: (j + -4)(j + -4) = 10 Calculate the square root of the right side: 3.16227766 Break this problem into two subproblems by setting (j + -4) equal to 3.16227766 and -3.16227766.Subproblem 1
j + -4 = 3.16227766 Simplifying j + -4 = 3.16227766 Reorder the terms: -4 + j = 3.16227766 Solving -4 + j = 3.16227766 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + j = 3.16227766 + 4 Combine like terms: -4 + 4 = 0 0 + j = 3.16227766 + 4 j = 3.16227766 + 4 Combine like terms: 3.16227766 + 4 = 7.16227766 j = 7.16227766 Simplifying j = 7.16227766Subproblem 2
j + -4 = -3.16227766 Simplifying j + -4 = -3.16227766 Reorder the terms: -4 + j = -3.16227766 Solving -4 + j = -3.16227766 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + j = -3.16227766 + 4 Combine like terms: -4 + 4 = 0 0 + j = -3.16227766 + 4 j = -3.16227766 + 4 Combine like terms: -3.16227766 + 4 = 0.83772234 j = 0.83772234 Simplifying j = 0.83772234Solution
The solution to the problem is based on the solutions from the subproblems. j = {7.16227766, 0.83772234}
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