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Simplifying j2 + -26j + 45 = 0 Reorder the terms: 45 + -26j + j2 = 0 Solving 45 + -26j + j2 = 0 Solving for variable 'j'. Begin completing the square. Move the constant term to the right: Add '-45' to each side of the equation. 45 + -26j + -45 + j2 = 0 + -45 Reorder the terms: 45 + -45 + -26j + j2 = 0 + -45 Combine like terms: 45 + -45 = 0 0 + -26j + j2 = 0 + -45 -26j + j2 = 0 + -45 Combine like terms: 0 + -45 = -45 -26j + j2 = -45 The j term is -26j. Take half its coefficient (-13). Square it (169) and add it to both sides. Add '169' to each side of the equation. -26j + 169 + j2 = -45 + 169 Reorder the terms: 169 + -26j + j2 = -45 + 169 Combine like terms: -45 + 169 = 124 169 + -26j + j2 = 124 Factor a perfect square on the left side: (j + -13)(j + -13) = 124 Calculate the square root of the right side: 11.135528726 Break this problem into two subproblems by setting (j + -13) equal to 11.135528726 and -11.135528726.Subproblem 1
j + -13 = 11.135528726 Simplifying j + -13 = 11.135528726 Reorder the terms: -13 + j = 11.135528726 Solving -13 + j = 11.135528726 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + j = 11.135528726 + 13 Combine like terms: -13 + 13 = 0 0 + j = 11.135528726 + 13 j = 11.135528726 + 13 Combine like terms: 11.135528726 + 13 = 24.135528726 j = 24.135528726 Simplifying j = 24.135528726Subproblem 2
j + -13 = -11.135528726 Simplifying j + -13 = -11.135528726 Reorder the terms: -13 + j = -11.135528726 Solving -13 + j = -11.135528726 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + j = -11.135528726 + 13 Combine like terms: -13 + 13 = 0 0 + j = -11.135528726 + 13 j = -11.135528726 + 13 Combine like terms: -11.135528726 + 13 = 1.864471274 j = 1.864471274 Simplifying j = 1.864471274Solution
The solution to the problem is based on the solutions from the subproblems. j = {24.135528726, 1.864471274}
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