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Simplifying 19j(5j + -7) = 15 Reorder the terms: 19j(-7 + 5j) = 15 (-7 * 19j + 5j * 19j) = 15 (-133j + 95j2) = 15 Solving -133j + 95j2 = 15 Solving for variable 'j'. Reorder the terms: -15 + -133j + 95j2 = 15 + -15 Combine like terms: 15 + -15 = 0 -15 + -133j + 95j2 = 0 Begin completing the square. Divide all terms by 95 the coefficient of the squared term: Divide each side by '95'. -0.1578947368 + -1.4j + j2 = 0 Move the constant term to the right: Add '0.1578947368' to each side of the equation. -0.1578947368 + -1.4j + 0.1578947368 + j2 = 0 + 0.1578947368 Reorder the terms: -0.1578947368 + 0.1578947368 + -1.4j + j2 = 0 + 0.1578947368 Combine like terms: -0.1578947368 + 0.1578947368 = 0.0000000000 0.0000000000 + -1.4j + j2 = 0 + 0.1578947368 -1.4j + j2 = 0 + 0.1578947368 Combine like terms: 0 + 0.1578947368 = 0.1578947368 -1.4j + j2 = 0.1578947368 The j term is -1.4j. Take half its coefficient (-0.7). Square it (0.49) and add it to both sides. Add '0.49' to each side of the equation. -1.4j + 0.49 + j2 = 0.1578947368 + 0.49 Reorder the terms: 0.49 + -1.4j + j2 = 0.1578947368 + 0.49 Combine like terms: 0.1578947368 + 0.49 = 0.6478947368 0.49 + -1.4j + j2 = 0.6478947368 Factor a perfect square on the left side: (j + -0.7)(j + -0.7) = 0.6478947368 Calculate the square root of the right side: 0.804919087 Break this problem into two subproblems by setting (j + -0.7) equal to 0.804919087 and -0.804919087.Subproblem 1
j + -0.7 = 0.804919087 Simplifying j + -0.7 = 0.804919087 Reorder the terms: -0.7 + j = 0.804919087 Solving -0.7 + j = 0.804919087 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + j = 0.804919087 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + j = 0.804919087 + 0.7 j = 0.804919087 + 0.7 Combine like terms: 0.804919087 + 0.7 = 1.504919087 j = 1.504919087 Simplifying j = 1.504919087Subproblem 2
j + -0.7 = -0.804919087 Simplifying j + -0.7 = -0.804919087 Reorder the terms: -0.7 + j = -0.804919087 Solving -0.7 + j = -0.804919087 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + j = -0.804919087 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + j = -0.804919087 + 0.7 j = -0.804919087 + 0.7 Combine like terms: -0.804919087 + 0.7 = -0.104919087 j = -0.104919087 Simplifying j = -0.104919087Solution
The solution to the problem is based on the solutions from the subproblems. j = {1.504919087, -0.104919087}
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