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Simplifying 2i2 + -26i + -41 = 0 Reorder the terms: -41 + -26i + 2i2 = 0 Solving -41 + -26i + 2i2 = 0 Solving for variable 'i'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -20.5 + -13i + i2 = 0 Move the constant term to the right: Add '20.5' to each side of the equation. -20.5 + -13i + 20.5 + i2 = 0 + 20.5 Reorder the terms: -20.5 + 20.5 + -13i + i2 = 0 + 20.5 Combine like terms: -20.5 + 20.5 = 0.0 0.0 + -13i + i2 = 0 + 20.5 -13i + i2 = 0 + 20.5 Combine like terms: 0 + 20.5 = 20.5 -13i + i2 = 20.5 The i term is -13i. Take half its coefficient (-6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. -13i + 42.25 + i2 = 20.5 + 42.25 Reorder the terms: 42.25 + -13i + i2 = 20.5 + 42.25 Combine like terms: 20.5 + 42.25 = 62.75 42.25 + -13i + i2 = 62.75 Factor a perfect square on the left side: (i + -6.5)(i + -6.5) = 62.75 Calculate the square root of the right side: 7.921489759 Break this problem into two subproblems by setting (i + -6.5) equal to 7.921489759 and -7.921489759.Subproblem 1
i + -6.5 = 7.921489759 Simplifying i + -6.5 = 7.921489759 Reorder the terms: -6.5 + i = 7.921489759 Solving -6.5 + i = 7.921489759 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + i = 7.921489759 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + i = 7.921489759 + 6.5 i = 7.921489759 + 6.5 Combine like terms: 7.921489759 + 6.5 = 14.421489759 i = 14.421489759 Simplifying i = 14.421489759Subproblem 2
i + -6.5 = -7.921489759 Simplifying i + -6.5 = -7.921489759 Reorder the terms: -6.5 + i = -7.921489759 Solving -6.5 + i = -7.921489759 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '6.5' to each side of the equation. -6.5 + 6.5 + i = -7.921489759 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + i = -7.921489759 + 6.5 i = -7.921489759 + 6.5 Combine like terms: -7.921489759 + 6.5 = -1.421489759 i = -1.421489759 Simplifying i = -1.421489759Solution
The solution to the problem is based on the solutions from the subproblems. i = {14.421489759, -1.421489759}
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