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Simplifying 5j = j2 + 2j + -3 Reorder the terms: 5j = -3 + 2j + j2 Solving 5j = -3 + 2j + j2 Solving for variable 'j'. Reorder the terms: 3 + 5j + -2j + -1j2 = -3 + 2j + j2 + 3 + -2j + -1j2 Combine like terms: 5j + -2j = 3j 3 + 3j + -1j2 = -3 + 2j + j2 + 3 + -2j + -1j2 Reorder the terms: 3 + 3j + -1j2 = -3 + 3 + 2j + -2j + j2 + -1j2 Combine like terms: -3 + 3 = 0 3 + 3j + -1j2 = 0 + 2j + -2j + j2 + -1j2 3 + 3j + -1j2 = 2j + -2j + j2 + -1j2 Combine like terms: 2j + -2j = 0 3 + 3j + -1j2 = 0 + j2 + -1j2 3 + 3j + -1j2 = j2 + -1j2 Combine like terms: j2 + -1j2 = 0 3 + 3j + -1j2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -3 + -3j + j2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -3j + 3 + j2 = 0 + 3 Reorder the terms: -3 + 3 + -3j + j2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -3j + j2 = 0 + 3 -3j + j2 = 0 + 3 Combine like terms: 0 + 3 = 3 -3j + j2 = 3 The j term is -3j. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3j + 2.25 + j2 = 3 + 2.25 Reorder the terms: 2.25 + -3j + j2 = 3 + 2.25 Combine like terms: 3 + 2.25 = 5.25 2.25 + -3j + j2 = 5.25 Factor a perfect square on the left side: (j + -1.5)(j + -1.5) = 5.25 Calculate the square root of the right side: 2.291287847 Break this problem into two subproblems by setting (j + -1.5) equal to 2.291287847 and -2.291287847.Subproblem 1
j + -1.5 = 2.291287847 Simplifying j + -1.5 = 2.291287847 Reorder the terms: -1.5 + j = 2.291287847 Solving -1.5 + j = 2.291287847 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + j = 2.291287847 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + j = 2.291287847 + 1.5 j = 2.291287847 + 1.5 Combine like terms: 2.291287847 + 1.5 = 3.791287847 j = 3.791287847 Simplifying j = 3.791287847Subproblem 2
j + -1.5 = -2.291287847 Simplifying j + -1.5 = -2.291287847 Reorder the terms: -1.5 + j = -2.291287847 Solving -1.5 + j = -2.291287847 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + j = -2.291287847 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + j = -2.291287847 + 1.5 j = -2.291287847 + 1.5 Combine like terms: -2.291287847 + 1.5 = -0.791287847 j = -0.791287847 Simplifying j = -0.791287847Solution
The solution to the problem is based on the solutions from the subproblems. j = {3.791287847, -0.791287847}
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