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Simplifying j2 + 4j + -122 = 0 Reorder the terms: -122 + 4j + j2 = 0 Solving -122 + 4j + j2 = 0 Solving for variable 'j'. Begin completing the square. Move the constant term to the right: Add '122' to each side of the equation. -122 + 4j + 122 + j2 = 0 + 122 Reorder the terms: -122 + 122 + 4j + j2 = 0 + 122 Combine like terms: -122 + 122 = 0 0 + 4j + j2 = 0 + 122 4j + j2 = 0 + 122 Combine like terms: 0 + 122 = 122 4j + j2 = 122 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 = 122 + 4 Reorder the terms: 4 + 4j + j2 = 122 + 4 Combine like terms: 122 + 4 = 126 4 + 4j + j2 = 126 Factor a perfect square on the left side: (j + 2)(j + 2) = 126 Calculate the square root of the right side: 11.22497216 Break this problem into two subproblems by setting (j + 2) equal to 11.22497216 and -11.22497216.Subproblem 1
j + 2 = 11.22497216 Simplifying j + 2 = 11.22497216 Reorder the terms: 2 + j = 11.22497216 Solving 2 + j = 11.22497216 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 = 11.22497216 + -2 Combine like terms: 2 + -2 = 0 0 + j = 11.22497216 + -2 j = 11.22497216 + -2 Combine like terms: 11.22497216 + -2 = 9.22497216 j = 9.22497216 Simplifying j = 9.22497216Subproblem 2
j + 2 = -11.22497216 Simplifying j + 2 = -11.22497216 Reorder the terms: 2 + j = -11.22497216 Solving 2 + j = -11.22497216 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 = -11.22497216 + -2 Combine like terms: 2 + -2 = 0 0 + j = -11.22497216 + -2 j = -11.22497216 + -2 Combine like terms: -11.22497216 + -2 = -13.22497216 j = -13.22497216 Simplifying j = -13.22497216Solution
The solution to the problem is based on the solutions from the subproblems. j = {9.22497216, -13.22497216}
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