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Simplifying j2 + -14j = -39 Reorder the terms: -14j + j2 = -39 Solving -14j + j2 = -39 Solving for variable 'j'. Reorder the terms: 39 + -14j + j2 = -39 + 39 Combine like terms: -39 + 39 = 0 39 + -14j + j2 = 0 Begin completing the square. Move the constant term to the right: Add '-39' to each side of the equation. 39 + -14j + -39 + j2 = 0 + -39 Reorder the terms: 39 + -39 + -14j + j2 = 0 + -39 Combine like terms: 39 + -39 = 0 0 + -14j + j2 = 0 + -39 -14j + j2 = 0 + -39 Combine like terms: 0 + -39 = -39 -14j + j2 = -39 The j term is -14j. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14j + 49 + j2 = -39 + 49 Reorder the terms: 49 + -14j + j2 = -39 + 49 Combine like terms: -39 + 49 = 10 49 + -14j + j2 = 10 Factor a perfect square on the left side: (j + -7)(j + -7) = 10 Calculate the square root of the right side: 3.16227766 Break this problem into two subproblems by setting (j + -7) equal to 3.16227766 and -3.16227766.Subproblem 1
j + -7 = 3.16227766 Simplifying j + -7 = 3.16227766 Reorder the terms: -7 + j = 3.16227766 Solving -7 + j = 3.16227766 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + j = 3.16227766 + 7 Combine like terms: -7 + 7 = 0 0 + j = 3.16227766 + 7 j = 3.16227766 + 7 Combine like terms: 3.16227766 + 7 = 10.16227766 j = 10.16227766 Simplifying j = 10.16227766Subproblem 2
j + -7 = -3.16227766 Simplifying j + -7 = -3.16227766 Reorder the terms: -7 + j = -3.16227766 Solving -7 + j = -3.16227766 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + j = -3.16227766 + 7 Combine like terms: -7 + 7 = 0 0 + j = -3.16227766 + 7 j = -3.16227766 + 7 Combine like terms: -3.16227766 + 7 = 3.83772234 j = 3.83772234 Simplifying j = 3.83772234Solution
The solution to the problem is based on the solutions from the subproblems. j = {10.16227766, 3.83772234}
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