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Simplifying j2 + 4j = 11 Reorder the terms: 4j + j2 = 11 Solving 4j + j2 = 11 Solving for variable 'j'. Reorder the terms: -11 + 4j + j2 = 11 + -11 Combine like terms: 11 + -11 = 0 -11 + 4j + j2 = 0 Begin completing the square. Move the constant term to the right: Add '11' to each side of the equation. -11 + 4j + 11 + j2 = 0 + 11 Reorder the terms: -11 + 11 + 4j + j2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + 4j + j2 = 0 + 11 4j + j2 = 0 + 11 Combine like terms: 0 + 11 = 11 4j + j2 = 11 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 = 11 + 4 Reorder the terms: 4 + 4j + j2 = 11 + 4 Combine like terms: 11 + 4 = 15 4 + 4j + j2 = 15 Factor a perfect square on the left side: (j + 2)(j + 2) = 15 Calculate the square root of the right side: 3.872983346 Break this problem into two subproblems by setting (j + 2) equal to 3.872983346 and -3.872983346.Subproblem 1
j + 2 = 3.872983346 Simplifying j + 2 = 3.872983346 Reorder the terms: 2 + j = 3.872983346 Solving 2 + j = 3.872983346 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 = 3.872983346 + -2 Combine like terms: 2 + -2 = 0 0 + j = 3.872983346 + -2 j = 3.872983346 + -2 Combine like terms: 3.872983346 + -2 = 1.872983346 j = 1.872983346 Simplifying j = 1.872983346Subproblem 2
j + 2 = -3.872983346 Simplifying j + 2 = -3.872983346 Reorder the terms: 2 + j = -3.872983346 Solving 2 + j = -3.872983346 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 = -3.872983346 + -2 Combine like terms: 2 + -2 = 0 0 + j = -3.872983346 + -2 j = -3.872983346 + -2 Combine like terms: -3.872983346 + -2 = -5.872983346 j = -5.872983346 Simplifying j = -5.872983346Solution
The solution to the problem is based on the solutions from the subproblems. j = {1.872983346, -5.872983346}
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