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Simplifying j2 + 28j = -31 Reorder the terms: 28j + j2 = -31 Solving 28j + j2 = -31 Solving for variable 'j'. Reorder the terms: 31 + 28j + j2 = -31 + 31 Combine like terms: -31 + 31 = 0 31 + 28j + j2 = 0 Begin completing the square. Move the constant term to the right: Add '-31' to each side of the equation. 31 + 28j + -31 + j2 = 0 + -31 Reorder the terms: 31 + -31 + 28j + j2 = 0 + -31 Combine like terms: 31 + -31 = 0 0 + 28j + j2 = 0 + -31 28j + j2 = 0 + -31 Combine like terms: 0 + -31 = -31 28j + j2 = -31 The j term is 28j. Take half its coefficient (14). Square it (196) and add it to both sides. Add '196' to each side of the equation. 28j + 196 + j2 = -31 + 196 Reorder the terms: 196 + 28j + j2 = -31 + 196 Combine like terms: -31 + 196 = 165 196 + 28j + j2 = 165 Factor a perfect square on the left side: (j + 14)(j + 14) = 165 Calculate the square root of the right side: 12.845232579 Break this problem into two subproblems by setting (j + 14) equal to 12.845232579 and -12.845232579.Subproblem 1
j + 14 = 12.845232579 Simplifying j + 14 = 12.845232579 Reorder the terms: 14 + j = 12.845232579 Solving 14 + j = 12.845232579 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + j = 12.845232579 + -14 Combine like terms: 14 + -14 = 0 0 + j = 12.845232579 + -14 j = 12.845232579 + -14 Combine like terms: 12.845232579 + -14 = -1.154767421 j = -1.154767421 Simplifying j = -1.154767421Subproblem 2
j + 14 = -12.845232579 Simplifying j + 14 = -12.845232579 Reorder the terms: 14 + j = -12.845232579 Solving 14 + j = -12.845232579 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + j = -12.845232579 + -14 Combine like terms: 14 + -14 = 0 0 + j = -12.845232579 + -14 j = -12.845232579 + -14 Combine like terms: -12.845232579 + -14 = -26.845232579 j = -26.845232579 Simplifying j = -26.845232579Solution
The solution to the problem is based on the solutions from the subproblems. j = {-1.154767421, -26.845232579}
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