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Simplifying 24 = 1i + 0.05i2 Solving 24 = 1i + 0.05i2 Solving for variable 'i'. Reorder the terms: 24 + -1i + -0.05i2 = 1i + -1i + 0.05i2 + -0.05i2 Combine like terms: 1i + -1i = 0 24 + -1i + -0.05i2 = 0 + 0.05i2 + -0.05i2 24 + -1i + -0.05i2 = 0.05i2 + -0.05i2 Combine like terms: 0.05i2 + -0.05i2 = 0.00 24 + -1i + -0.05i2 = 0.00 Begin completing the square. Divide all terms by -0.05 the coefficient of the squared term: Divide each side by '-0.05'. -480 + 20i + i2 = 0 Move the constant term to the right: Add '480' to each side of the equation. -480 + 20i + 480 + i2 = 0 + 480 Reorder the terms: -480 + 480 + 20i + i2 = 0 + 480 Combine like terms: -480 + 480 = 0 0 + 20i + i2 = 0 + 480 20i + i2 = 0 + 480 Combine like terms: 0 + 480 = 480 20i + i2 = 480 The i term is 20i. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20i + 100 + i2 = 480 + 100 Reorder the terms: 100 + 20i + i2 = 480 + 100 Combine like terms: 480 + 100 = 580 100 + 20i + i2 = 580 Factor a perfect square on the left side: (i + 10)(i + 10) = 580 Calculate the square root of the right side: 24.083189158 Break this problem into two subproblems by setting (i + 10) equal to 24.083189158 and -24.083189158.Subproblem 1
i + 10 = 24.083189158 Simplifying i + 10 = 24.083189158 Reorder the terms: 10 + i = 24.083189158 Solving 10 + i = 24.083189158 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + i = 24.083189158 + -10 Combine like terms: 10 + -10 = 0 0 + i = 24.083189158 + -10 i = 24.083189158 + -10 Combine like terms: 24.083189158 + -10 = 14.083189158 i = 14.083189158 Simplifying i = 14.083189158Subproblem 2
i + 10 = -24.083189158 Simplifying i + 10 = -24.083189158 Reorder the terms: 10 + i = -24.083189158 Solving 10 + i = -24.083189158 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + i = -24.083189158 + -10 Combine like terms: 10 + -10 = 0 0 + i = -24.083189158 + -10 i = -24.083189158 + -10 Combine like terms: -24.083189158 + -10 = -34.083189158 i = -34.083189158 Simplifying i = -34.083189158Solution
The solution to the problem is based on the solutions from the subproblems. i = {14.083189158, -34.083189158}
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