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Simplifying 0.5i2 + 4i + -10 = 0 Reorder the terms: -10 + 4i + 0.5i2 = 0 Solving -10 + 4i + 0.5i2 = 0 Solving for variable 'i'. Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. -20 + 8i + i2 = 0 Move the constant term to the right: Add '20' to each side of the equation. -20 + 8i + 20 + i2 = 0 + 20 Reorder the terms: -20 + 20 + 8i + i2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + 8i + i2 = 0 + 20 8i + i2 = 0 + 20 Combine like terms: 0 + 20 = 20 8i + i2 = 20 The i term is 8i. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8i + 16 + i2 = 20 + 16 Reorder the terms: 16 + 8i + i2 = 20 + 16 Combine like terms: 20 + 16 = 36 16 + 8i + i2 = 36 Factor a perfect square on the left side: (i + 4)(i + 4) = 36 Calculate the square root of the right side: 6 Break this problem into two subproblems by setting (i + 4) equal to 6 and -6.Subproblem 1
i + 4 = 6 Simplifying i + 4 = 6 Reorder the terms: 4 + i = 6 Solving 4 + i = 6 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + i = 6 + -4 Combine like terms: 4 + -4 = 0 0 + i = 6 + -4 i = 6 + -4 Combine like terms: 6 + -4 = 2 i = 2 Simplifying i = 2Subproblem 2
i + 4 = -6 Simplifying i + 4 = -6 Reorder the terms: 4 + i = -6 Solving 4 + i = -6 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + i = -6 + -4 Combine like terms: 4 + -4 = 0 0 + i = -6 + -4 i = -6 + -4 Combine like terms: -6 + -4 = -10 i = -10 Simplifying i = -10Solution
The solution to the problem is based on the solutions from the subproblems. i = {2, -10}
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