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Simplifying (-0.125j + 6)(20j + 4) = 0 Reorder the terms: (6 + -0.125j)(20j + 4) = 0 Reorder the terms: (6 + -0.125j)(4 + 20j) = 0 Multiply (6 + -0.125j) * (4 + 20j) (6(4 + 20j) + -0.125j * (4 + 20j)) = 0 ((4 * 6 + 20j * 6) + -0.125j * (4 + 20j)) = 0 ((24 + 120j) + -0.125j * (4 + 20j)) = 0 (24 + 120j + (4 * -0.125j + 20j * -0.125j)) = 0 (24 + 120j + (-0.5j + -2.5j2)) = 0 Combine like terms: 120j + -0.5j = 119.5j (24 + 119.5j + -2.5j2) = 0 Solving 24 + 119.5j + -2.5j2 = 0 Solving for variable 'j'. Begin completing the square. Divide all terms by -2.5 the coefficient of the squared term: Divide each side by '-2.5'. -9.6 + -47.8j + j2 = 0 Move the constant term to the right: Add '9.6' to each side of the equation. -9.6 + -47.8j + 9.6 + j2 = 0 + 9.6 Reorder the terms: -9.6 + 9.6 + -47.8j + j2 = 0 + 9.6 Combine like terms: -9.6 + 9.6 = 0.0 0.0 + -47.8j + j2 = 0 + 9.6 -47.8j + j2 = 0 + 9.6 Combine like terms: 0 + 9.6 = 9.6 -47.8j + j2 = 9.6 The j term is -47.8j. Take half its coefficient (-23.9). Square it (571.21) and add it to both sides. Add '571.21' to each side of the equation. -47.8j + 571.21 + j2 = 9.6 + 571.21 Reorder the terms: 571.21 + -47.8j + j2 = 9.6 + 571.21 Combine like terms: 9.6 + 571.21 = 580.81 571.21 + -47.8j + j2 = 580.81 Factor a perfect square on the left side: (j + -23.9)(j + -23.9) = 580.81 Calculate the square root of the right side: 24.1 Break this problem into two subproblems by setting (j + -23.9) equal to 24.1 and -24.1.Subproblem 1
j + -23.9 = 24.1 Simplifying j + -23.9 = 24.1 Reorder the terms: -23.9 + j = 24.1 Solving -23.9 + j = 24.1 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '23.9' to each side of the equation. -23.9 + 23.9 + j = 24.1 + 23.9 Combine like terms: -23.9 + 23.9 = 0.0 0.0 + j = 24.1 + 23.9 j = 24.1 + 23.9 Combine like terms: 24.1 + 23.9 = 48 j = 48 Simplifying j = 48Subproblem 2
j + -23.9 = -24.1 Simplifying j + -23.9 = -24.1 Reorder the terms: -23.9 + j = -24.1 Solving -23.9 + j = -24.1 Solving for variable 'j'. Move all terms containing j to the left, all other terms to the right. Add '23.9' to each side of the equation. -23.9 + 23.9 + j = -24.1 + 23.9 Combine like terms: -23.9 + 23.9 = 0.0 0.0 + j = -24.1 + 23.9 j = -24.1 + 23.9 Combine like terms: -24.1 + 23.9 = -0.2 j = -0.2 Simplifying j = -0.2Solution
The solution to the problem is based on the solutions from the subproblems. j = {48, -0.2}
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