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Simplifying -4j2 + 1 = -5j + -5j2 Reorder the terms: 1 + -4j2 = -5j + -5j2 Solving 1 + -4j2 = -5j + -5j2 Solving for variable 'j'. Reorder the terms: 1 + 5j + -4j2 + 5j2 = -5j + -5j2 + 5j + 5j2 Combine like terms: -4j2 + 5j2 = 1j2 1 + 5j + 1j2 = -5j + -5j2 + 5j + 5j2 Reorder the terms: 1 + 5j + 1j2 = -5j + 5j + -5j2 + 5j2 Combine like terms: -5j + 5j = 0 1 + 5j + 1j2 = 0 + -5j2 + 5j2 1 + 5j + 1j2 = -5j2 + 5j2 Combine like terms: -5j2 + 5j2 = 0 1 + 5j + 1j2 = 0 Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + 5j + -1 + j2 = 0 + -1 Reorder the terms: 1 + -1 + 5j + j2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 5j + j2 = 0 + -1 5j + j2 = 0 + -1 Combine like terms: 0 + -1 = -1 5j + j2 = -1 The j term is 5j. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5j + 6.25 + j2 = -1 + 6.25 Reorder the terms: 6.25 + 5j + j2 = -1 + 6.25 Combine like terms: -1 + 6.25 = 5.25 6.25 + 5j + j2 = 5.25 Factor a perfect square on the left side: (j + 2.5)(j + 2.5) = 5.25 Calculate the square root of the right side: 2.291287847 Break this problem into two subproblems by setting (j + 2.5) equal to 2.291287847 and -2.291287847.Subproblem 1
j + 2.5 = 2.291287847 Simplifying j + 2.5 = 2.291287847 Reorder the terms: 2.5 + j = 2.291287847 Solving 2.5 + j = 2.291287847 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + j = 2.291287847 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + j = 2.291287847 + -2.5 j = 2.291287847 + -2.5 Combine like terms: 2.291287847 + -2.5 = -0.208712153 j = -0.208712153 Simplifying j = -0.208712153Subproblem 2
j + 2.5 = -2.291287847 Simplifying j + 2.5 = -2.291287847 Reorder the terms: 2.5 + j = -2.291287847 Solving 2.5 + j = -2.291287847 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + j = -2.291287847 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + j = -2.291287847 + -2.5 j = -2.291287847 + -2.5 Combine like terms: -2.291287847 + -2.5 = -4.791287847 j = -4.791287847 Simplifying j = -4.791287847Solution
The solution to the problem is based on the solutions from the subproblems. j = {-0.208712153, -4.791287847}
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